Question

the diameter of a sphere is 4 centimeters. which represents the volume of the sphere?
$\frac{32}{3}pi\text{ cm}^3$
$8pi\text{ cm}^3$
$\frac{64}{3}pi\text{ cm}^3$
$16pi\text{ cm}^3$

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter. Given diameter $d = 4$ cm, so $r=\frac{d}{2}=\frac{4}{2}=2$ cm.

Step2: Use the volume formula

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 2$ into the formula: $V=\frac{4}{3}\pi\times(2)^{3}=\frac{4}{3}\pi\times8=\frac{32}{3}\pi$ $cm^{3}$.

Answer:

$\frac{32}{3}\pi$ $cm^{3}$