tripling the radius of a sphere results in increasing its volume by a factor of
A) 27π
B) 27
C) 9
D) 3

Question

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = 4/3 πr^3.
Tripling the radius means: new radius = 3r.
Substituting into the formula: 
New Volume = 4/3 π(3r)^3 = 4/3 π27r^3 = 36πr^3

So, the factor by which the volume increases is: 
New Volume/Old Volume = 36πr^3 /4/3 πr^3 = 36/4 = 9.
Therefore, the answer is B) 27, as this is the cube of the increase factor (3).

Tripling the Radius of a Sphere Results in Increasing Its