How to Find the Height of a Cylinder

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Finding the Volume for a Sphere with a Radius of 4: How-To & Steps

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 Steps to Solve
  • 2:07 Applications
  • 4:19 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we'll see how to find the height of a cylinder by manipulating the formula for the volume of a cylinder. We'll also look at a practical application of this formula.

Steps to Solve

Before we can learn how to find the height of a cylinder, we need to quickly review some vocabulary. A cylinder is a three-dimensional object with two equal-sized circular ends. These equal-sized circular ends are called bases. The height of a cylinder is the distance between the two circular bases.


One more vocabulary word, and that is the volume of a cylinder. The volume is the amount of space the cylinder takes up, and we have a nice formula for finding the volume of a cylinder. If V is the volume of a cylinder, h is the height, and r is the radius of the circular bases, then we have the following:

V = πr2h

Or volume is equal to πr2 * height.

At this point, you may be wondering why we are talking about the formula for finding volume of a cylinder when we are interested in finding the height of a cylinder, and that's a fair question! Let's answer it!

The reason we are looking at the volume formula is because we can manipulate this formula to derive a formula for the height of a cylinder.

We begin with:

V = πr2h

If we divide both sides by πr2, we have:

V ÷ (πr2) = h

If we interchange the sides of this equation, we are left with:

h = V ÷ (πr2)

Ta-da! We now have a formula we can use to find the height of a cylinder. That is, if we know the volume, V, of a cylinder and the radius, r, of the circular base of a cylinder, we can find the height, h. We have derived the formula:

h = V ÷ (πr2)

Where V is the volume of the cylinder and r is the radius of the circular bases of the cylinder; so the height of a cylinder is equal to the volume of the cylinder divided by πr2.



Okay, time to put this newly-learned knowledge to use. Suppose you have recently inherited a farm that has a huge old silo on it. You decide to fix up the silo so that you can put it back into use. Part of this fixer-upper job involves attaching a ladder to the side of the silo that goes all the way up to the top of the silo.

How Long Should the Ladder Be?

As you can see, to determine how long the ladder should be, we need to know the height of the silo. You probably also noticed that the silo is in the shape of a cylinder, which is perfect, because we know how to find the height of a cylinder.

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 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

Transferring credit to the school of your choice

Not sure what college you want to attend yet? 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.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account