Question

1. if the volume of a sphere is ( 36pi mathrm{cm}^{3} ), what is its radius?

a. ( 2 mathrm{~cm} )
b. ( 4 mathrm{~cm} )
c. ( 1 mathrm{~cm} )
d. ( 3 mathrm{~cm} )

Explanation:

Step1: Recall the volume formula of a sphere

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

Step2: Substitute the given volume into the formula

Given \(V = 36\pi\), we have \(36\pi=\frac{4}{3}\pi r^{3}\).

Step3: Solve for \(r^{3}\)

Divide both sides of the equation by \(\pi\): \(36=\frac{4}{3}r^{3}\). Then multiply both sides by \(\frac{3}{4}\): \(r^{3}=36\times\frac{3}{4}=27\).

Step4: Solve for \(r\)

Take the cube - root of both sides: \(r = \sqrt[3]{27}=3\).

Answer:

D. 3 cm