Question

find the volume of the sphere. v = ? π cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Determine the radius of the sphere

From the problem, the diameter \(d = 6\space cm\). Since \(r=\frac{d}{2}\), then \(r=\frac{6}{2}=3\space cm\).

Step3: Substitute the radius into the formula

Substitute \(r = 3\) into \(V=\frac{4}{3}\pi r^{3}\). We get \(V=\frac{4}{3}\pi\times(3)^{3}\).
First, calculate \((3)^{3}=3\times3\times3 = 27\). Then \(V=\frac{4}{3}\pi\times27\).
Since \(\frac{4}{3}\times27=4\times9 = 36\).

Answer:

\(36\)