Question

if the volume of a sphere is $36\pi cm^{3}$, what is its radius?
a. 2 cm
b. 4 cm
c. 3 cm
d. 1 cm

Explanation:

Step1: Write the volume formula for a sphere

The volume formula for 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 substitute into the formula: \(36\pi=\frac{4}{3}\pi r^{3}\).

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:

C. 3 cm