Question

Two cones are similar. The surface area of the larger cone is 65π square inches. The surface area of the smaller cone is 41.6π square inches. The radius of the smaller cone is 6.4 inches.

What is the radius of the larger cone?

8 inches
10 inches
11.52 inches
14.4 inches

Answer 1

Surface areas scale as the square of the linear scale factor. Let s = (small linear)/(large linear). Then s^2 = 41.6π / 65π = 41.6/65 = 0.64, so s = √0.64 = 0.8.

Since 6.4 = s · (radius of larger), the larger radius = 6.4 / 0.8 = 8 inches.

Answer: 8 inches.