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 to denote the radius of either circle, and we use 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 and a height of is

Surface Area of a Circular Cylinder: The surface area of a circular cylinder with a radius of and a height of is

Practice Problems:

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

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

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