Question

what is the volume of a sphere with a radius of 21 units?
a. 9261π units³
b. 12,348π units³
c. 588π units³
d. 37,044π units³

Explanation:

Step1: Recall volume formula

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius.

Step2: Substitute radius value

Given $r = 21$, we substitute it into the formula: $V=\frac{4}{3}\pi\times(21)^{3}$.
First, calculate $(21)^{3}=21\times21\times21 = 9261$.
Then, $V=\frac{4}{3}\pi\times9261$.
$\frac{4\times9261}{3}\pi=4\times3087\pi = 12348\pi$.

Answer:

B. $12,348\pi$ units$^{3}$