Practice!

Sample Problem

We have a cylinder and 3 squares with side lengths equal to the cylinder’s radius. Given that the height of the cone is two times the length of its radius, find the ratio of the total area of the 3 squares to the area of the lateral face.

  : π

Solution

Let’s call the radius of the cylinder, r. Thus, the lateral surface area is 2πr × 2r = 4πr2. The area of one square is r2, so the area of 3 squares is 3r2. Thus, the ratio of the area of the 3 squares to the area of the lateral face is

 .