Question

A bowling ball made for a child has 1/2 times the radius of an adult bowling ball. It is made of the same material (and therefore has the same mass per unit volume).

By what factor is the mass of the child’s ball reduced compared with the adult ball?

Answer 1

The mass of the child’s bowling ball is reduced by a factor of 8 compared to an adult’s bowling ball because the volume and mass are proportional to the cube of the radius.

Step-by-step explanation:

The mass of the child’s bowling ball is reduced compared with the adult ball by the factor of the cube of the radius ratio. Since the child’s bowling ball has 1/2 the radius of the adult's ball, we square this to find the scale factor for the volume and hence the mass (assuming uniform density). The volume and mass of a sphere scale with the cube of the radius, so if the child’s ball has half the radius of the adult’s ball, it has (1/2)^3 = 1/8 the volume and thus 1/8 the mass. Therefore, the mass of the child’s bowling ball is reduced by a factor of 8 compared to an adult’s bowling ball.