Back To Course

Geometry: High School15 chapters | 160 lessons

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn why soda cans are cylinders and the method by which you can discover how much soda can fit inside by finding the volume. You will also learn about finding a cylinder's surface area.

Cylinders are popular shapes. Defined, a **cylinder** is a three-dimensional object with two round flat bases and one curved side. Picture a soda can and you are looking at a cylinder. These types of cans hold not only soda but also juices and other types of drinks as well. Walk into any grocery store and you will find tons of cylinders holding all kinds of goodies inside.

When it comes to cylinders, there are two measurements that you need to be concerned about. If you look at your soda cans, you will notice that they are all the same height and that the circles that make up the tops and bottoms are all the same size as well. This is because they have the same height as well as the same radius, which is the distance between the middle of the circle to the edge. It is these two measurements that determine the size of a cylinder. We label the height with *h* and the radius with *r* to make it easier for us when we are using the formulas for surface area and volume. Both formulas use both measurements.

The formula for surface area gives you the total area of all the surfaces together. Let's say you want to decorate your soda can with colorful wrapping paper. The formula for surface area will let you know how much paper you need. The formula looks like this:

Surface Area = 2 * pi * *r* * (*r* + *h*)

As long as you have your radius and height, you can go ahead and plug those values into your formula to find your answer for surface area. Let's see how this works if we have a soda can that is 6 inches high with a radius of 2 inches. We can label our *h* as 6 inches and our *r* as 2 inches. We then plug these numbers into our formula.

Surface Area = 2 * 3.14 * 2 * (2 + 6)

I've replaced the pi with its approximation of 3.14, and now all I need to do is to evaluate to find my answer. So I add the 2 and the 6 to get 8. I then multiply the 2 with the 3.14 with the 2 and then with the 8 to get my answer of 100.48 inches squared.

Surface Area = 2 * 3.14 * 2 * 8

Surface Area = 100.48 inches squared

My answer ends with my measuring unit squared, because area is always squared.

Now, if I wanted to find out how much soda the same soda can holds, I would use the formula for volume, the amount of space inside a three-dimensional object. The formula for the volume of a cylinder looks like this.

Volume = pi * *r*^2 * *h*

Again, if I had my radius and height, I can go ahead and plug those numbers in to find my answer. I already know that the soda can we are using has a height of 6 inches and a radius of 2 inches, so I can plug those numbers into the formula.

Volume = 3.14 * 2^2 * 6

I then go ahead and evaluate to find my answer. I square the 2 to get 4. I then multiply the 3.14, the 4, and the 6 together to get an answer of 75.36 inches cubed.

Volume = 3.14 * 4 * 6

Volume = 75.36 inches cubed

My answer here ends with my measuring units cubed, because volume is always cubed.

What have we learned? We've learned that **cylinders** are three-dimensional objects with two round flat bases and one curved side. Soda cans are real-world examples of cylinders. The only two measurements you need to find surface area and volume are the height and the radius. The formula for surface area is Surface Area = 2 * pi * *r* * (*r* + *h*), and the formula for volume is Volume = pi * *r*^2 * *h*. Once you have your height and radius, all you need is to plug in these numbers into your formula to find your answer.

After concluding this lesson, you should be able to:

- Define the 3-dimensional object- cylinder
- Understand the formulas for measuring cylinders
- Identify how to measure the volume of a cylinder

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
5 in chapter 11 of the course:

Back To Course

Geometry: High School15 chapters | 160 lessons

- Planes and the Polyhedron: Definition and Example 3:52
- What Are Platonic Solids? - Definition and Types 4:39
- Prisms: Definition, Area & Volume 6:12
- Pyramids: Definition, Area & Volume 7:43
- What Are Cylinders? - Definition, Area & Volume 5:09
- Spheres: Definition, Area & Volume 5:22
- Go to High School Geometry: Geometric Solids

- OAE Prekindergarten Subtests I & II (036/037): Study Guide & Practice
- NES Essential Academic Skills: Study Guide & Practice
- OAE Foundations of Reading (090): Study Guide & Practice
- OSAT School Psychologist Exam (CEOE) (033): Study Guide & Practice
- Praxis Physical Education - Content & Design (5095): Study Guide & Practice
- Exercise & Nutrition
- Early Childhood Development Overview
- Overview of Culture
- Basic Instructional Strategies for Physical Education
- Careers in Healthcare
- AFOQT Cost
- What Does the HESI A2 Nursing Exam Consist of?
- How to Learn Pharmacology for NCLEX
- What Are Considered Higher-Level Questions on the NCLEX?
- How to Study for NCLEx in 2 Weeks
- How Hard Is the ASVAB
- How Long is the HESI A2 Nursing Exam?

- Gender Identity Discrimination in the Workplace: Definition, Laws & Cases
- Teaching Math to Students with Autism
- Aerobic Gram-Positive Bacilli: Characteristics, Types & Examples
- Income Elasticity of Demand in Microeconomics
- What Are the Benefits of Hiring Veterans?
- Practical Application: Creating an Inclusive Workplace Environment for Veterans Infographic
- How to Accommodate Religious Dietary Restrictions for Your Employees
- Veterans in the Workplace: Work Style & Characteristics
- Quiz & Worksheet - Phonics Instruction
- Quiz & Worksheet - Effects of Disabilities on Self & Others
- Quiz & Worksheet - Concept Generalization Teaching Methods
- Quiz & Worksheet - Parental Involvement in IEPs
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- HiSET Science: Prep and Practice
- Finding & Applying for Student Loans
- Grade Level Flashcards
- UExcel Social Psychology: Study Guide & Test Prep
- PSAT Prep: Tutoring Solution
- MTLE Business: Data Interpretation & Management
- MTEL Business: Basic Concepts of Microeconomics
- Quiz & Worksheet - Proximate Cause & Law
- Quiz & Worksheet - Theories of Natural Law
- Quiz & Worksheet - Virginia Company
- Quiz & Worksheet - Art Criticism
- Quiz & Worksheet - The Fundamental Orders of Connecticut

- Aerophones: Types & Examples
- Overview of the Poultry & Livestock Industries
- Engineering Competitions for High School
- How to Calculate College GPA
- Geometry Math Games
- Books for Guided Reading
- Illinois Common Core Standards
- How to Pass the CPA Exam
- eBooks vs. Textbooks
- How to Pass 6th Grade
- Creative Nonfiction Writing Exercises
- NSF Dissertation Grant Types and Application Tips

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject