Proportional Reasoning

Question

A sphere has a radius of 3 and a hemisphere has a radius of 6. Compare the ratio of the volume of the sphere to the volume of the hemisphere. 

Answer 1

V_sphere : V_hemisphere = 4/3 π*3³ : 2/3 π*6³ = 2(3/6)³ = 1/4

This makes sense, since if the radius of a sphere doubles, the volume grows by a factor of 8. But we only have a large hemisphere, so the ratio is twice 1/8 or 1/4