Writing a cause and effect essay
Holt Mathematics Algebra 2 Homework Help Online
Wednesday, April 1, 2020
Byui Calendar Software is a Must Have For All Students
Byui Calendar Software is a Must Have For All StudentsThe byui calendar serves as a tutor scheduling system. This helps all of the students in organizing their lessons so that they can easily make lessons around their schedules. The byui calendar allows for students to look up and schedule their tutoring so that they can avoid long and confusing lines of students waiting to see the tutor.For students who use this online tutoring center, they will be able to sign up to tutor online at the convenient of their own home. After students have made their appointments, they can communicate with the tutor over the Internet. This can be a very helpful feature for students who work in groups or with a lot of other students.Students can even arrange tutoring in a more convenient manner. There are software programs available on the Internet that allow for students to use their computers to make the needed adjustments on their own. This will ensure that students will not have to wait to see their tutor or worry about when it is best to come back for their next tutoring session.If a student is unable to come to the tutoring center until after his or her regular tutoring appointment, then this will help to make sure that there is a timely schedule for the students. Many students have problems trying to schedule lessons around their schedules. However, the byui calendar helps students to create a schedule that works for all students in the tutoring center.A tutor scheduling software will also be useful for those students who are trying to deal with many students and need to get ready for a few tutoring sessions in a day. This can be very difficult for students who work in groups or are assigned to work with a lot of other students. Some students may find that they get along better when they are tutored individually.For those students who live in the tutoring center, the byui calendar will help them to easily manage their schedule. It will also help students to see how much time they have to spend in the tutoring center. With the help of this software program, students will be able to organize their studies for the day.By knowing how many students will be in the tutoring center and how many students will be available, students will be able to plan around these numbers and make sure that they have a full schedule to fit in with. In addition, the byui calendar helps students make sure that they will be able to be ready for their next class at the scheduled time. Once they have made sure that they will be available, they can begin to schedule their next class.With the help of the blue calendar, students will be able to organize their lessons and time management around their schedules. They will also be able to see how much time they have to work on their assignments. As students adjust to the byui calendar, they will also be able to set up their schedules in a more efficient manner.
Saturday, March 21, 2020
The Tutor Academy of Lahore
The Tutor Academy of LahoreAre you going to attend the Lahore Tutor Academy? If so, you will be joining a school that is known for its excellent education and high standards.The school, which is also known as the Lahore International School, is located in Pakistan's capital city of Lahore. Its curriculum is a blend of English, Maths, and Science. This school also has a large number of students who come from more than 40 countries across the world. Students who have an interest in business and accounting are also part of the school.The school also provides students with additional learning opportunities. In addition to providing English, Maths, and Science, it also offers Arts and crafts classes for students in grades 6 and up. This school also serves a very large population of students in Pakistan and is one of the oldest private English Language Schools in the country. Classes are held seven days a week and all students are required to attend every day of the school.One of the best things about this school is that its curriculum is tailored specifically for students of various different ages. They are also able to go home after their lessons to continue with their life after school. Since the school has its own library, students can study at their own pace and without pressure. They can also create and use their own tests and quizzes for their exams and can keep up with their studies as well.The school was founded in 1967 and provides a high quality international education for students who speak English. It is very well known for its highly skilled teachers and lecturers, who are able to answer any questions of students. Another reason why students like the school is because of the support that they receive from their parents who can drop them off during the day when they are attending classes. These schools are also very well managed by their administration staff, who provide support to students both at home and at school.One of the most popular subjects at t he school is tutoring. There are also many institutions and colleges where students are able to learn English through the tutoring program. This program offers English classes for students who are unable to attend regular classes due to certain reasons such as physical disabilities or mental problems. There are many tutors that are available in Pakistan to work with students who want to learn English as a second language.The main purpose of enrolling in this school is to study English. Students are also given a chance to interact with many other students from different cultures. Although the student community is a mix of many different backgrounds, the academic standards are high and the students are able to obtain a diploma in English and Mathematics.
Friday, March 6, 2020
How to Recover from a Disappointing Midterm Grade
How to Recover from a Disappointing Midterm Grade The transition from high school to college is a big one. Anecdotal evidence shows it is not uncommon for new freshmen to struggle with midterm exams. Even if you did well in high school, the new environment, increased academic rigor, and newfound freedom of college can decrease your academic performance. It can be difficult to balance the new experiences and the need to study. If you receive a disappointing grade on a midterm, it may be a warning sign that you need to find your life-school balance in order to recover by the end of the semester. The good news is, it is possible to recover from a disappointing midterm grade. With a little positivity, analysis, and hard work, you can lift yourself out of a poor grade situation. The following tips can help: Dont dwell on your bad midterm grade You earned a bad grade on an important testnow you need to accept it and move on. Dont waste time dwelling on your midterm grade; instead, work to fix the problem going forward. You can take an evening to drown your disappointment in a pint of Ben and Jerrys, but after that, focus on recovering from your subpar grade. Dont let this setback deter you from earning good grades. Identify problem subject areas To move forward, youll need to have a plan. The first thing you need to do is figure out what you need help with specifically. What particular content areas gave you trouble? Were you underprepared, or did you mistakenly think you understood the information? Did you make careless mistakes? Do you need help with time management or study skills? A tool that you may find helpful for this is an exam wrapper. Exam wrappers are questionnaires that help you identify problem areas on exams and identify ways you can improve your preparation for the next one. For example, if you received a C- on your college algebra midterm, an exam wrapper could help you identify that quadratic equations and augmented matrices are the concepts in which you are weakest. Furthermore, taking college algebra diagnostic tests or practice exams could provide additional insight (and extra practice) into your academic strengths and weaknesses. Seek academic help Dont be afraid to ask for help when you need it. If you do poorly on your midterm, you might want to make an appointment to see your professor. He or she can help you further identify your problem areas and can help explain the concepts that you do not understand. In addition, he or she may also suggest avenues for bringing up your grade, whether its an extra paper or an extra credit project. Is your chemistry grade less than ideal? You may also want to seek out chemistry tutors who can provide individualized attention you may not receive in a college lecture hall. Dont be afraid to seek out a study group or tutorials, as well. Prioritize your tasks and manage your time Figure out what you need to do to improve your gradethen do it. Although you should take time to eat, sleep, and otherwise take care of yourself, remember that you still have a relatively short period of time to buckle down and improve your grade before the semester ends. Evaluate your schedule and other commitments, and prioritize accordingly in order to reach your goal. Dont give up Bombing a midterm is not the end of the world. As F. Scott Fitzgerald said, Never confuse a single defeat with a final defeat. There are always opportunities to learn from and improve on a bad grade. The second half of the term is a very short amount of time in the grand scheme of things. Keep at ityou can do it! Even though you may have fallen short on your midterm, there is still time to recover. Believe it or not, this is a common occurrence, and it is important to move forward confidently. Accept what happened, figure out what you need help with, manage your remaining time, and stay focused through the end of the semester. A poor grade can help you develop necessary time management skills and lead to you find your balance between your social life and academic responsibilities.
Thursday, March 5, 2020
Career Advice for the Young Introvert - Introvert Whisperer
Introvert Whisperer / Career Advice for the Young Introvert - Introvert Whisperer Career Advice for the Young Introvert Guest Author September 28, 2015 Career Development, Self-Promotion 2 responses Being nervous when entering a new job or the workforce, in general, is normal, and totally fine. If you donât quite know where youâre going yet, here are a few things to know. Actions speak louder than words. Weâve all heard this once, twice, a thousand times, but it holds truth. Your actions will always speak louder than your words, so make them count. When it comes to your career, what you do is more important than what you say, since following through with a plan will build more trust than consistently saying youâll do something. You do not have to constantly ask questions, or give updates on where you are. While it may be a good habit to get into, when your work is getting done without being asked, your reputation will build itself. Basically, to make a lasting impression you donât have to speak above the crowd. Silence does not equal compliance. Simple enough, but silence can sometimes be mistaken for a âyesâ in the workplace, and itâs important to make sure your opinion and voice are heard. Being able to have a voice in your workplace gives employees the ability to help fix conflict and make the work environment more inviting. It also gives the opportunity for feedback, which is important for self-growth. When you feel like youâre being unheard or ignored, your work or motivation can be negatively impacted. To succeed in your career, youâll have to be able to explain your point of view and let others know, and you owe it to yourself to make sure youâre clear on what you want or why your idea is a good one. Youâre not a stereotype of the creepy. What I mean is, donât let the idea that youâre antisocial keep you from a social job. While working from home seems like an introverts dream, you do not have to adhere to that stereotype, and you donât have to let anyone box you in like that. Being shy and quiet are related to both introverts and âcreepyâ people, not all suffer from social anxiety or shyness. In fact, some of the best jobs for introverts include Critical Care Nurses, Criminologists, and Interpreters and Translators. Introverts have characteristics of being observant, collected, and decisive, making it easy for us to thrive in social environments just as well as our extroverted counterparts. Being âshyâ can be used to your advantage. So youâre quiet. So you donât actively engage seek out conversation. So what? Being shy is said to make people more approachable, or easier to talk to because you donât come off as threatening. If youâre shy, youâre also more likely to think before you act, clearly forming your ideas and plans before setting anything in motion. This gives people a form of stability and makes you more desirable because it builds that trust. Shy people also know how to problem solve on their own. Not saying this trait is exclusive to shy people, itâs a trait a lot of great workers have, but if weâre rolling with the stereotype, shy introverts internalize. Internalizing isnât always the best practice, but shyer people tend to develop an easier ability to overcome obstacles; especially if youâve fought against your own shyness. Remember your own values. Itâs a hard world, and a lot of the times you will have your values and morals put to the test. So, the last piece of advice I have is to remember where you stand. Advancing your career is obviously important, especially if youâve set high standards, but donât compromise yourself for a job. Wanting to adjust to being the right fit for is also normal, but losing grasp on whatâs important to you isnât worth the negative consequences that can follow. What do you prioritize in your career? Have you set a standard for yourself yet, or are you going to wait until you decide what you want? Keeping in mind your values and planning a course of action from there is the surest way to check yourself before you wreck what youâve built up. Everything is subjective and case-by-case because personalities are fluid. Though I donât know you personally, I hope you can take away something helpful from these five pieces of advice. Guest Author: Sacha
The Importance of Nutrition for Personal Training
The Importance of Nutrition for Personal Training How You Should be Fuelling Your Sports Coaching Sessions, According to a Personal Trainer ChaptersKeep Your Eye on the BallWhy You Should Never Skip MealsThe Importance of a Good Nightâs SleepChanging Your DietThe fitness industry covers many things, from senior fitness to corrective exercise and group exercise programs to spa facilities. One service that is gaining popularity is private training with an accredited personal gym instructor.Once you have taken the plunge and hired a personal trainer, youâll realise that their fitness expertise covers much more than physical exercise.As a fitness professional, your personal trainer will provide you with a complete fitness training program which covers your workouts as well as the healthy habits you should adopt.Working towards your goals with a personal fitness instructor is about changing your lifestyle so that you can be the healthiest version of yourself, so private sports coaching is about changing your mentality as much as it is about getting fit.Itâs no secret that exercise has many health benefits.In addition to the numerous gruelling exams they have to sit to get a personal trainer certification, in order to get certified and become a personal trainer, each fitness coach must also be highly knowledgeable when it comes to the nutritional aspect of exercise science.The aim of a personal trainer is not only to provide high-quality services but to also encourage and motivate you throughout your journey to a healthier you.When you set your fitness goals, your personal trainer will use their program design skills to provide you with a fitness program which is tailored to your training objectives, current lifestyle, cardio strength and your physiology (based on your body composition fitness assessment).Sometimes, in order to be sure that their services are right for you, trainers will ask you about your needs and goals before accepting you as a student.Whether youâre aiming to lose weight, improve your cardiovascular endurance training, get some guidance with your resistance training, be show n how to become a yoga or Pilates pro, run faster, tone your figure or just fancy a change from group fitness classes near me, your personal trainer will show you the best route to success as an athlete through one on one coaching to train your body to the next level.It is essential that you stick rigorously to their training and nutritional advice if you want to see the results of your efforts quickly. CalumDrama School Entrance Teacher 5.00 (15) £50/h1st lesson free!Discover all our tutors ToriSpanish Teacher 5.00 (1) £15/h1st lesson free!Discover all our tutors OliviaSchool support Teacher 5.00 (2) £21/h1st lesson free!Discover all our tutors MarkESOL (English) Teacher 4.76 (17) £20/h1st lesson free!Discover all our tutors YuweiChinese Teacher 4.33 (6) £19/h1st lesson free!Discover all our tutors JenniferMusic reading Teacher 5.00 (1) £30/h1st lesson free!Discover all our tutors LouiseAutoCAD Teacher 5.00 (3) £60/h1st lesson free!Discover all our tutors RickyPercus sion Teacher 5.00 (7) £35/h1st lesson free!Discover all our tutors NicolasGuitar Teacher 5.00 (2) £35/h1st lesson free!Discover all our tutors MyriamOrganic chemistry Teacher 5.00 (13) £20/h1st lesson free!Discover all our tutors JonathanEconomics Teacher 5.00 (9) £40/h1st lesson free!Discover all our tutors Oluwakemi imoleMaths Teacher 5.00 (1) £30/h1st lesson free!Discover all our tutors AlexPhysics Teacher 5.00 (1) £50/h1st lesson free!Discover all our tutors AdamSinging Teacher 5.00 (14) £48/h1st lesson free!Discover all our tutors ValentiniMusic reading Teacher 5.00 (2) £50/h1st lesson free!Discover all our tutors MilenaMaths Teacher 5.00 (5) £25/h1st lesson free!Discover all our tutors RashmiEconomics Teacher 5.00 (1) £35/h1st lesson free!Discover all our tutorsKeep Your Eye on the BallTo get yourself on track to achieving your goals, you'll first need to find a personal trainer. You can look online or ask in your local gyms or health clubs.Your personal sp orts coach will show you a range of training techniques and give you expert advice on how you should be fuelling your workouts, but their expertise can only come to fruition if you are motivated and determined in achieving your goal.By sticking to the diet plan given to you by your personal fitness trainer, you greatly increase your chances of success in your programme.Keep your eye on the prize, no matter what ¦ source: Visualhunt - Francesco GallarottiIf youâre aiming to shed a few pounds, your coach will teach you about the importance of knowing the nutritional value of your food.They will help you to make the right decisions as you learn to make informed choices about the food you eat.So, donât be tempted by foods with a high sugar and salt content. Eating more nutrient-rich foods will keep you satisfied and keep your cravings at bay â" you just need to know what to choose!The most important thing is the very first kilo you lose, because this is a confirmation that all yo ur hard work is paying off!As your mentor, your personal trainer will continue to motivate you as the weight drops off and they will never make you feel disheartened if some weeks are more challenging than others.Your coach will be able to help you find the right balance when it comes to your eating habits, and they will never put you in a situation where your fitness nutrition becomes an obsession.They will also propose alternatives to snacking or binging so that youâre not consuming too many calories throughout the day, as this could affect your progress.All of these methods contribute to a healthier lifestyle and can not only be used in your fitness career but also throughout your life to keep you in shape.Why You Should Never Skip MealsWorking out can help you slim down â" everyone knows that.However, many people mistakenly think that depriving their body of certain meals throughout the day will help them lose the weight more quickly.Your personal trainer, on the other hand, will tell you that skipping meals is a deadly sin.Whatever your programme and goals, every private fitness coach will strongly advise against fasting because of its effects on your body.The media talks about calories as something to keep as low as possible, however, calories give you the energy to fuel your workouts, and avoiding them could have serious consequences as your body will not be able to sustain a high level of physical activity and recover effectively.So, your personal trainer will advise you to continue eating at regular mealtimes, but theyâll tell you to either reduce your portion sizes or banish certain foods from your plate.This way, you wonât be starving your body of vital nutrients and youâll find it far easier to get used to your new eating habits.Take time to prepare and enjoy your food ¦ source: Pixabay - StockSnapYour coach may also be able to give you valuable advice on many other related topics, such as the best food diary apps.Depending on your perso nal health and fitness objectives, your trainer will be able to guide you when it comes to making the right food choices â" particularly when youâre looking to build muscle mass.As well as informing you on which foods to avoid, your coach will also show you how to choose more nutrient-rich foods that will give your body what it needs.By reducing your portions, you will allow your body to use up its natural fat stores without feeling hungry!The Importance of a Good Nightâs SleepWellbeing is about maintaining an overall balance of work and rest.Your personal trainer will stress the importance of taking rest days and getting plenty of sleep to help your body recover and get stronger for future personal training sessions.When you exercise with your private coach, youâll feel fatigue in your muscles as well as general tiredness. Itâs important that you donât put bedtime off until itâs too late to get a sufficient amount of sleep since like skipping meals, your body will not get a chance to replace everything it has used during the day.Getting an early night before a hard workout is equally as important.Regulating your sleeping pattern will not only benefit your workouts but help you feel more energised throughout the day.Once you start sessions with a personal trainer, youâll likely be advised to go to bed before 10pm and sleep for a minimum of 8 hours every night.This, like changing your eating habits, is another part of adopting a healthier and more rewarding lifestyle. You will soon find that better nutrition and a good workout will improve the quality of your sleep so you will be getting more out of your eight hours.Changing Your DietStart by ruling out processed foods and ready meals.All you have to do is remove unhealthy choices from your shopping basket, and as your personal trainer will remind you, this part is essential to getting the results youâre aiming for.Of course, weâve all given into the temptation to food that is so easy to prep are.For busy people who have little time to cook from scratch as well as shoppers who just want cheap and easy fast-food on a day out, easy meals seem to be everywhere, and thatâs why itâs so difficult to escape the temptation.Take a list to the supermarket and stick to it to avoid unhealthy impulse buys ¦ source: Pixabay - StockSnapThis part of your training will require a lot of willpower, and you should bear in mind that choosing fast food over fresh food will only undo your hard work at the gym, and make it harder to achieve success in your training.Processed foods are full of chemical preservatives, added sugars and other nasty ingredients that your body will not thank you for.So, make sure you read food labels and seriously consider what you are putting into your body â" it doesnât like being poisoned!Choosing to remove these foods from your diet and cooking healthier, more natural meals will leave you feeling noticeably better in your day-to-day life as well as during your workouts.Donât feel bad about spending a bit of extra time at the supermarket to find out about healthier options â" just enjoy your continuing education about what is right for your body!Increase Protein IntakeIf youâve asked your coach to help you lose fat and gain muscle mass, youâll be advised to try and eat more protein.Regardless of your goals, upping your intake of protein can be beneficial as it helps repair your muscle tissue following a workout, as well as aiding general recovery.Eating chicken and turkey is particularly good for athletes, as they are rich in protein and low in fat. Fish and pulses are also good options.Meat can be quite expensive, so your coach will help you with finding good sources of protein that are within your budget and taste great!Reduce Your Intake of Sugary and Fatty FoodsThis is another key point for personal fitness training.We always hear about the dangers of sugar and fat in the media, but how harmful are they really? And what ca n you do to avoid them? Your personal trainer will be able to clarify this for you by explaining why certain foods are unhealthy.Youâll find out that some sugars are your worst enemy â" so you shouldnât eat sweets, but this doesnât mean you have to avoid fruit!The science behind sugar and exactly why itâs bad for weight loss will all become clear once you begin your training programme.Itâs the same case for fatty foods. Lessen your intake of saturated fats, but continue to eat the âhealthyâ fats found in dairy and nuts.Your personal trainer will take pleasure in helping you get to grips with the complex world of sports nutrition, as they explain key points and answer any questions you have along the way.Search for a 'personal trainer near me' now!
What is it Like to Attend Bucknell University
What is it Like to Attend Bucknell University Jared earned his bachelors degree in biomedical engineering from Bucknell University. He specializes in geometry tutoring, biology tutoring, and a number of other subjects. Below, he shares his experience at Bucknell University: Describe the campus setting and transportation options. Jared: Bucknell is a pretty rural campus. Theres a beautiful, historic, and quaint downtown. Both the campus and the town of Lewisburg, PA are extremely safe. Theres a bus that takes you to certain places around campus and to grocery stores and medical centers. Theres also a late-night bus that circulates between the upper part of campus and downtown. Luckily, at Bucknell you will never need to drive from one place on campus to another or to downtown; everything is within walking distance. How available are the professors, academic advisers, and teaching assistants? Jared:Professors, advisers, and TAs are all available. All of the professors are primarily there to teach, not to do research. So, their favorite part of their job is teaching you during class or office hours. Advisers are professors in your department, so they will be equally available. TAs also always hold office hours. How would you describe the dorm liferooms, dining options, location, socialization opportunities with other students? Jared:Dorm life is good. Bucknell works really hard during orientation to connect you with your peers and your RA. Buildings have tight communities that end up being groups of friends. If you join a residential college, youll have two upperclassmen in your hall that youll live with all year long and a class that youre guaranteed to have with a lot of your hallmates. Bucknell is a small enough campus that none of the first year dorms are in bad spots. Socialization is also easy. There are common areas in every dorm, and each dorm hall has its own programs that connect you with other people. Your first year, you have an unlimited dining plan in Bostwick Marketplace, or the cafeteria with an open buffet, which is great because you can socialize with people you know all of the time. Some people like the food there so much that they get the unlimited meal plan all four years at Bucknell. Which majors/programs are best represented and supported? Jared:Every major and program is really well supported. Some are smaller than others, and some have more or less funding, but theyre all supported. How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Jared:Greek life is huge on Bucknells campus; around two thirds of the campus joins. The good thing about it is that you cant join a Greek organization until your sophomore year, so you have a lot of time to decide whether or not its something that fits with what you want out of your college experience. I chose not to get involved in Greek life, even though many of my friends did. Theres a lot of other ways to make friends aside from Greek life. I didnt have a hard time making friends at Bucknell. Orientation does a great job at breaking down the awkward barriers of making new friends. At Bucknell, almost everyone is in the same boat as you; they know almost no one and they want to find friends. I found sports a good way to make friends, but other people have made friends through video games, the arts, their major, and other avenues. I continued to meet people all four years by joining different clubs, my on-campus jobs, and through other chance interactions. How helpful are the Career Centerand other student support services? Jared:The career center works really hard at Bucknell. Some really awesome companies, like Deloitte, Merck, General Electric, Microsoft, and many others recruit at Bucknell. Ive heard of people getting offers from other companies, too, like Amazon, Google, and Morgan Stanley. The career center does a great job of connecting you with alumni in your industry to get you internships, jobs, and mentoring advice; all you have to do is put in the necessary effort. How are the various study areas such aslibraries, the student union, and dorm lounges? Jared:Study areas at Bucknell are great. There is a gorgeous library, a cool coffee shop, and buildings on campus open all hours of the day so you can just camp out and do homework in them. I went into computer labs in certain buildings during the evening hours and they were usually empty because other people didnt think to go there. The places are never so overcrowded so that you cant find a spot, but if youre looking for a quiet spot during certain peak times of the day or the year, it can be challenging. Describe the surrounding town. Jared:Downtown Lewisburg is a true gem that far too few people take advantage of during their time at Bucknell. It has great places to eat, cute places to shop, and quaint places to hang out. How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Jared:There are about 3,600 undergraduate students at Bucknell. My biggest classes were my introductory chemistry, physics, biology, and engineering classes, which were around 60 people. I had a total of eight classes with over 50 students in them, and the rest of the classes I had at Bucknell were around 20-25 students per class. Every professor I had still remembers my name; so, even if you have bigger classes, they will still get to know you if you put in the effort. Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Jared:Three years after my introductory biology course, I went to a campus event called Chrysalis, which is attended by most of Bucknells students and faculty. Its a semi-formal event with hors doeuvres and a concert. The band never played their most famous song, so it was obvious that they were going to come back out for an encore. A minute later, a music video of their most famous song came on. Then, as the chorus came and they walked on stage, I started looking around, making ridiculous faces, pretending to be surprised. I caught the eye of my favorite professor from my first year at Bucknell while making a ridiculous face. He made an equally ridiculous face back at me also pretending to be surprised. I laughed for the rest of the song. Check out Jareds tutoring profile.The views expressed in this article do not necessarily represent the views of Varsity Tutors.
Volume Formula
Volume Formula Volume Formula: Volume is defined as the space occupied within a 3-dimensional solid object. Volume of an object is also referred to as its Capacity. Volume is one of the most important and commonly used measuring formula to calculate the space enclosed within the boundaries of a 3-dimensional object. The objects which have 3 dimensions of length, width and height are known as a 3-dimensional object. Examples of such figures include cube, cuboid, prism, sphere, cone, pyramid etc. The standard measuring units for volume are cubic centimeters, cubic meters, cubic foot, cubic inch, liters, etc. The figure below shows us various 3-dimensional objects and the spaces enclosed within them. Before we calculate the volume of each of the above figures, we must know how to convert one unit of volume to another unit. Conversion of Volume: In order to convert volume from one unit to another unit, we should be aware of the standard conversion between the units. For example, if we want to convert 1 cubic yard to cubic feet, then we must first know the standard conversion between yard and feet. 1 yard = 3 feet Now, a volume of 1 cubic yard implies 1yard * 1 yard * 1 yard Now to convert it to cubic feet and considering 1 yard is equal to 3 feet, we get: Volume of 1 cubic yard implies = 3 feet * 3 feet * 3 feet = 27 cubic feet. Therefore, 1 cubic yard = 27 cubic feet. Example: Convert 5 cubic meters to liters. The standard unit conversion between cubic meters and liters is: 1 cubic meter = 1000 liters Hence, 5 cubic meters = 5 * 1000 = 5000 liters. Volume Formula for Various Shapes: Calculating volume is a very commonly done procedure, and this process is done in our daily life quite often. If we need to measure the space within a rectangular box, then we must know the volume formula for that shape and similarly to be able to know the amount of water that can fit into a bottle, we must measure the space enclosed within the bottle. Now let us calculate the volume formula for different geometry shapes with different sizes. 1)Volume of a Box (Cuboid): A box is also considered a Cuboid or a rectangular prism, and the volume of a box is the volume or space enclosed within a box. As shown in the figure below, a box figure has length, width and height at right angles and the faces of the box or cuboid are usually rectangles. A cuboid as shown in the figure below has 6 faces, 8 vertices and 12 edges. If the dimensions of the box are given as length l, width w and height h, then the Volume of the box is given by the formula as shown below: Volume of the Box, V = length * width * height. Therefore, V = lwh Example: Find the volume of the box whose length is 12 inches, width is 8 inches and height is 7 inches. Given that length, l = 12 inches Width, w = 8 inches Height, h = 7 inches Therefore, Volume of the Box, V = length * width * height == V = 12 * 8 * 7 = 672 inches3 This implies, Volume of the Box = 672 cubic inches. 2)Volume of a Cube: A cube is a 3-dimensional figure whose faces are all square faces. A cube has 6 congruent square faces, 12 edges and 8 vertices. A cube is also known as a regular hexahedron. Since a cube consists of all equal or congruent squares, hence its side are of equal length as well. If the side length of a cube is s, then the Volume of a Cube, V = s * s * s. Therefore, V = s3 Example: What is the volume of a cube of side length 5cm? Given the side length of a cube, s = 5cm Volume of a Cube, V = s3 == Therefore, Volume, V = (5cm)3 = 125cm3 or 125 cubic centimeters. 3)Volume of a Cone: A cone is a geometric shape which has a circular base, and a single vertex (also known as apex). If the apex of the cone is exactly over the center of the circular base, then such a cone is known as the Right Cone. If the apex of the cone is not exactly over the center of the base, then such a cone is known as the Oblique Cone. For a given Cone, if the radius of the circular base is r, and height (or altitude) is h, then the Volume of the Cone is given by the equation below: Volume of a Cone, V =1/3 * * (radius)2 * height == Volume, V = 1/3 * * r2 * h Example: What is the Volume of a Cone whose radius is 7 inches and height is 8 inches? Given that radius, r = 7 inches and height, h = 8 inches. Volume of the Cone, V = 1/3 * * r2 * h = 1/3 * 3.14 * 72 * 8 = 410.3 inches3 4)Volume of a Sphere and a Hemisphere: A sphere is a 3-dimensioanl geometric figure which has no edges (sides) or vertices (corners). It is a perfectly symmetrical shape which has all its points on the surface equidistant from the center. If a sphere has a radius r, then the Volume of the Sphere is given by the equation below: Volume of a Sphere, V = 4/3 * * (radius)3 == Volume, V = 4/3 * * r3 When a sphere is cut into half, then we get a Hemisphere. Volume of a Hemisphere = 1/2 * (Volume of Sphere) = 1/2 * 4/3 * * r3 Therefore, Volume of a Hemisphere, V = 2/3 * ???? * r3 Example: Find the volume of a sphere whose radius is 10m. If the sphere is cut into half, then what is the volume of the hemisphere? Given that the radius of the sphere, r = 10m Volume of the Sphere, V = 4/3 * * r3 = 4/3 * 3.14 * (10)3 Therefore, Volume of the Sphere, V = 4186.7 m3 If the sphere is cut into half, we get a hemisphere. Volume of a Hemisphere = 2/3 * * r3 = 2/3 * 3.14 * (10)3 Therefore, Volume of a Hemisphere, V = 2093.3 m3 5)Volume of a Cylinder: A cylinder is a solid closed figure which has two congruent parallel circular bases that are connected by a curved surface. A cylinder has 2 bases that are circular in shape and are parallel to each other. Since they are circular, the bases have radius. These circular bases are connected by a curved surface and the line joining the centers of the circular bases is known as the Axis. The perpendicular distance between the 2 circular bases is known as the height or the altitude. In our daily life, a cylinder is a very commonly observed geometric shape. We usually find cylinders which are called Right Cylinders and the ones which are slant in their position, known as the Oblique Cylinders as shown in the diagram below. If the 2 bases are exactly above one another and the axis is at right angles to the base, then that cylinder is known as the Right Cylinder. If the 2 bases are not exactly above one another and the axis is not at right angles to the base, then that cylinder is known as the Oblique Cylinder. For a given Right or Oblique Cylinder, if the radius of the circular base is r and height (or altitude) which is the perpendicular distance between the 2 bases is h then the Volume of the Cylinder is given by the equation below: Volume of a Cylinder, V = ???? * (radius)2 * height == Volume, V = * r2 * h Example: Calculate the Volume of a Cylinder whose radius is 6cm and height is 9cm. Given that radius, r = 6cm and height, h = 9cm. Volume of the Cylinder, V = * r2 * h = 3.14 * 62 * 9 = 1017.36 cm3 6)Volume of a Pyramid: A pyramid is a 3-dimensional solid which has a base (which can be of any polygon), and has three or more triangular faces meeting at a single vertex (also known as the apex). Volume of a pyramid is the amount of space contained within the pyramid. Based on the base polygon we have different kinds of pyramids. If the base of a pyramid is a square, then we get a Square Pyramid. If the base of the pyramid is a triangle, then we get a Triangular Pyramid. Volume of any Pyramid can be calculated using the formula, V = 1/3 * (Base Area) * (Height) Volume of a Square Pyramid: If the side length of the square base is a and the perpendicular distance from the vertex (apex) to the center of the base is h, then the Volume of the Square Pyramid can be calculated by the equation below: Volume of a Pyramid, V = 1/3 * (Area of the base) * HeightSo, therefore, Volume of the Square Pyramid V = 1/3 * a2 * h Example:Find the volume of the square pyramid whose side is 4m and height is 6m. Given that the side length, a = 4m Height, h = 6m Volume of the Square Pyramid, V = 1/3 * a2 * h = 1/3 * (4)2 * 6 Therefore, volume of the Pyramid, V = 32m3 Volume of the Triangular Pyramid: If the base of a pyramid is a triangle, then that pyramid is known as a Triangular Pyramid. Usually the triangle at the base has equal sides, thus making it an equilateral triangular pyramid or a regular triangular pyramid. But if the sides of the base triangle are not equal, then we get an irregular base pyramid. Volume of a Triangular Pyramid = 1/3 * Base Area * Height Given the base of a Triangular pyramid is an equilateral triangle, and the side length is a and the perpendicular distance from the vertex (apex) to the center of the base is h. Since the base is an equilateral triangle of side length a, hence its base area is 3/4 * a2 Therefore, Volume of an Equilateral (Regular) Triangular Pyramid = 1/3 * 3/4 * a2 * h Example: Calculate the volume of a regular triangular pyramid whose triangle side length is 5m and height is 8m. Since it is mentioned that it is a regular triangular pyramid, hence the base is an equilateral triangle. Given that the side length, a = 5m and height, h = 8m Volume of an Equilateral Triangular Pyramid = 1/3 * 3/4 * a2 * h = 1/3 * 3/4 * 52 * 8 = 28.9 m3 Hence, the volume is 28.9 m3. 7) Volume of a Prism: A prism is a 3-dimensional solid object with flat faces which has identical bases (or ends) which are parallel to each other. The prisms have the same cross-section all along their length. Since a prism is a polyhedron, it does not contain any curved sides. All its faces are flat, and all the edges are straight lines. Based on the cross-section of the prism, there are various types of them. For instance, if the cross-section along the length of a prism is a square, it is a Square Prism. If the cross-section along its length is a triangle, then it is a Triangular Prism. Volume of a Prism, V = Base Area * Height of the prism. The base area of the prism depends on the type of base the prism has. Volume of a Square Prism: Given a prism which has a square base of side length s, and the height of the prism is h. Volume of the Square Prism = Base Area * Height == s2 * h Volume of a Square Prism, V = s2 * h Example: Calculate the volume of a square prism whose base length is 4m and height is 5m. Given that the base side length, s = 4m and height, h = 5m Volume of a Square Prism, V = s2 * h == V = (4m)2 * 5m = 80m3 Therefore, the volume of the given square prism is 80 cubic meters. Volume of a Triangular Prism: Given a prism which has a triangular base of side length s and the height of the base triangle is d. The height of the prism is given to be h. Volume of a Triangular Prism = Base Area * Height (Base Area of a triangle = 1/2 * base * height = 1/2 * s * d) Therefore, Volume of a Triangular Prism, V = 1/2 * s * d * h Example: Calculate the volume of a triangular prism whose base triangle length is 5m, height of the triangle is 3m and height of the prism is 8m. Given that the base side length, s = 5m, height of the triangular base, d = 3m and height of the prism, h = 8m. Volume of a Triangular Prism, V = 1/2 * s * d * h = 1/2 * 5m * 3m * 8m = 60m3 Therefore the volume of the given triangular prism is 60 cubic meters.
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