Consider the ratio of the surface area of a sphere to its volume.What happens to this ratio if the diameter of the sphere increases by a factor of 3?
A) Decreases by a factor of 9
B) Increases by a factor of 3
C) Decreases by a factor of 3
D) Increases by a factor of 9
E) Stays the same

Question

Quizplus · Accepted Answer

The ratio of surface area to volume of a sphere is given by 4πr^2/3πr^3 = 4/r. If the diameter of the sphere increases by a factor of 3, then its radius increases by a factor of 3/2. Therefore, the new ratio is 4/(3/2) = 8/3, which is 1/3 of the original ratio. So, the ratio decreases by a factor of 3.

Consider the Ratio of the Surface Area of a Sphere