Volume increases by the ____ of the diameter, and surface area increases by ____ of the diameter.
A) square; doubling
B) square; the cube
C) cube; the square
D) cube; the cube
E) none of these is the correct answer

Question

Quizplus · Accepted Answer

The volume of a sphere is given by (4/3)πr^3, where r is the radius (which is half the diameter). When the diameter doubles, the radius doubles as well, resulting in an increase of (2^3) = 8 times the original volume, which is a cube of the diameter. 
The surface area of a sphere is given by 4πr^2, which is proportional to the square of the diameter. When the diameter doubles, the radius doubles as well, resulting in an increase of (2^2) = 4 times the original surface area, which is a square of the diameter.

Volume Increases by the ____ of the Diameter, and Surface