math question i do not understand

Question

The weight of a synthetic ball varies directly with the cube of its radius. A ball with a radius of 2 inches weighs

0.80

pounds. Find the weight of a ball of the same material with a​ 3-inch radius.

Answer 1

W = kr³

k is a constant. Use the given information to find k.

k = W/r³ = 0.80/(2³) lbs/in³ = 0.1 lbs/in³

With W in pounds, r in inches, and k in lbs/in³,

W = 0.1 r³

Now plug in r = 3 inches and get the weight.