Question

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

Explanation:

Step1: Find sphere radius

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

Step2: Apply volume formula

Volume of sphere: $V = \frac{4}{3}\pi r^3$
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 (Option A)