The next 3D shape we shall look at is the circular cylinder (also called the “right circular cylinder” by the GRE for its right angles):

Circular Cylinder: A 3D shape that has a circle for both bases and a perpendicular line connecting the center of those bases.

Now, it follows from the definition that a circular cylinder’s top and bottom circles will be the same size. So we use r to denote the radius of either circle, and we use h to denote the height of the cylinder. Without further ado, we present:

Volume of a Circular Cylinder: The volume of a right circular cylinder with a radius of r and a height of h is \pi r^2h.

Why does this formula make sense?

Surface Area of a Circular Cylinder: The surface area of a circular cylinder with a radius of r and a height of h is 2\pi r^2 + 2\pi r h. 

Why does this formula make sense?

Practice Problems:

1. The cylinder below has a radius of 3 and a height h of 6. Find AC.

Answer

2. The surface area of a right circular cylinder is 24\pi and its radius is 2. What is the height of the cylinder?

Answer

3. The surface area of a cylinder is twice its volume. Its radius equals its height. What is the volume of the cylinder?

Answer

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