Question

the diameter of a sphere is 4 centimeters. which represents the volume of the sphere?
$\frac{32}{3}\pi$ cm³
$8\pi$ cm³
$\frac{64}{3}\pi$ cm³
$16\pi$ cm³

Explanation:

Step1: Find radius from diameter

Radius $r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2$ cm

Step2: Apply sphere volume formula

Volume formula: $V = \frac{4}{3}\pi r^3$
Substitute $r=2$: $V = \frac{4}{3}\pi (2)^3 = \frac{4}{3}\pi \times 8 = \frac{32}{3}\pi$

Answer:

$\frac{32}{3}\pi$ cm³ (the first option)