Suppose the radius of a sphere is halved. How does the sphere's new volume compare with its former volume?
A) The sphere's new volume is one-half of the former volume.
B) The sphere's new volume is one-fourth of the former volume.
C) The sphere's new volume is one-eighth of the former volume.
D) The sphere's new volume is the same as the former volume.

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 halved, the new volume becomes $\frac{4}{3}\pi (\frac{r}{2})^3 = \frac{4}{3}\pi \frac{r^3}{8} = \frac{1}{8}$ of the original volume, making the new volume one-eighth of the former volume.

Suppose the Radius of a Sphere Is Halved