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

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

.