Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-If the radius of a sphere is doubled, by what factor will the volume change?
A) 2
B) 8
C) 6
D) 4

Question

Quizplus · Accepted Answer

The volume of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$. If the radius is doubled, the new volume becomes $V' = \frac{4}{3}\pi (2r)^3 = \frac{4}{3}\pi 8r^3 = 8 \times \frac{4}{3}\pi r^3$, which means the volume increases by a factor of 8.

Simplify the Rational Expression