Question

1. what happens to the volume of a sphere if its radius is halved?

a. the volume is halved.
b. the volume stays the same.
c. the volume is reduced to one - fourth.
d. the volume is reduced to one - eighth.

Explanation:

Step1: Volume formula of sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\).

Step2: New radius

If the radius is halved, the new radius \(r_{new}=\frac{r}{2}\).

Step3: New volume

The new volume \(V_{new}=\frac{4}{3}\pi(\frac{r}{2})^{3}=\frac{4}{3}\pi\frac{r^{3}}{8}=\frac{1}{8}\times\frac{4}{3}\pi r^{3}\).
Since \(V = \frac{4}{3}\pi r^{3}\), then \(V_{new}=\frac{1}{8}V\).

Answer:

D. The volume is reduced to one - eighth.