Determine volume of sphere

Question

With a ruler, Diamond determines the diameter of a golf ball to be 4.2 centimeters (a radius of 2.1 cm) and the diameter of a practice softball to be 8.4 centimeters (a radius of 4.2 cm). Diamond erroneously claims that the softball has twice the volume of the golf ball. In a short paragraph, explain Diamonds misconceptions. Use the formula for the volume of a sphere to determine the volume of both the golf ball and the softball in cubic centimeters and then compare their volumes.

(Hint:   Golf Ball Volume  V = 4/3 π r³ ;   V = 4/3 ∙ (3.14) ∙ (2.1)³ )

(Hint:   Softball Volume    V = 4/3 π r³ ;   V = 4/3  ∙ (3.14) ∙ (4.2)³ )

Answer 1

The important part in the hint is that the volume of a sphere (or any other solid, for that matter) is proportional to the cube of linear dimensions, e.g. the radius.