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:

`(m_3)/(m_2)= ((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 ((3 in)^3)/((2 in)^3)= (5605.60 p) (3^3)/(2^3)=18919 pounds`