Question

The weight of a synthetic ball varies directly with the cube of its radius. a ball with a radius of 2 inches weighs 5.605.60 pounds. find the weight of a ball of the same material with a​ 3-inch radius.

Answer 1

The weight of the ball m is directly proportional to the cube of the radius, $r^3$. This means that the ratio between the weight of the ball with radius 3-in and 2-in should be equal to the ratio between the cubes of the two radii:
$\frac{m_3}{m_2}= \frac{(3 in)^3}{(2 in)^3}$
So we can find the weight of the ball when its radius is 3 inches:
$m_3 = m_2 \frac{(3 in)^3}{(2 in)^3}= (5605.60 p) \frac{3^3}{2^3}=18919 pounds$