Question

the radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units?

(\frac{3}{4}pi(6)^{2})

(\frac{4}{3}pi(6)^{3})

(\frac{3}{4}pi(12)^{2})

(\frac{4}{3}pi(12)^{3})

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume formula 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 that \(r = 6\) units. Substitute \(r = 6\) into the formula \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi(6)^{3}\).

Answer:

\(\frac{4}{3}\pi(6)^{3}\) (the second option)