Question

1. a sphere has a radius of 6 cm. what is its volume in terms of π?

a. 216π cm³
b. 432π cm³
c. 288π cm³
d. 144π cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \(r = 6\space cm\). Substitute \(r=6\) into the formula: \(V=\frac{4}{3}\pi(6)^{3}\).
First, calculate \(6^{3}=6\times6\times6 = 216\).
Then, \(V=\frac{4}{3}\pi\times216\).
Since \(\frac{4}{3}\times216=\frac{4\times216}{3}=4\times72 = 288\).

Answer:

C. \(288\pi\space cm^{3}\)