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Lesson 7: Volume

# Cylinder volume & surface area

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r². Learn how to use these formulas to solve an example problem. Created by Sal Khan.

## Want to join the conversation?

• What is the equation for surface area?
• For a cylinder there is 2 kinds of formulas the lateral and the total.
the lateral surface area is just the sides the formula for that is 2(pi)radius(height).
the formula for the total surface area is 2(pi)radius(height) + 2(pi)radius squared.
• whats a TT ?
• if you are entering in terms of pi, just type p after your answer and it'll automatically convert thanks to khan academy :)
• what is the value of pi
• Pi is an infinite number, but 3.14 is usually used in place of pi.
• How do you solve for the radius of a cylinder when you are not given the diameter but you have the height and the volume?
• Note that the radius is simply half the diameter.
The formula for the volume of a cylinder is:
V = Π x r^2 x h
"Volume equals pi times radius squared times height."
Now you can solve for the radius:
V = Π x r^2 x h <-- Divide both sides by Π x h to get:
V / (Π x h) = r^2 <-- Square root both sides to get:
sqrt(V / Π x h) = r
• I know this is weird, but now I really want some pie
• Happens to everyone. ;)
• I'm confused. I get how you do surface area of a circle and why you have to do it twice, but I don't get how or what Sal did with the part in the middle. Can anybody help?
• To calculate the surface area of the middle part of the cylinder, I like to think of it as a rectangle. The area of a rectangle is length x width.

In this case, length = the height of the cylinder and width = the circumference of the end of the cylinder (the circle).

The length is given, and the width can be calculated using the formula for circumference of a circle. Once you have both values, just multiply l x w to find the area, then add it to the area of the two circles to find the total surface area.

It might help to picture a can of soup - imagine you use a can opener to remove the top & bottom. Then imagine you take the can and cut it from top to bottom. If you flattened it out, you would have a rectangle. The cut side would be the height of the can, and the other side would be the part that wrapped around the top or bottom of the can.

Hopefully this helps make sense why that side is the same length as the circumference of the circle at the end of the cylinder!
• Think im more confused now than when I started
• Probably just pressure or something. I was a little intimidated when I saw that this video was like 8 minutes, but I turned out fine.
• What is the cylinder volume formula? I didn't see him put it in the video.
• The volume of a cylinder = π r² h

Hope this helps.