Question

a sphere has a volume of $288pi cm^{3}$. what is the radius of the sphere? a. 5 cm b. 8 cm c. 4 cm d. 6 cm

Explanation:

Step1: Write the formula for the volume 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 \(V = 288\pi\), we have \(288\pi=\frac{4}{3}\pi r^{3}\).

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

Divide both sides of the equation by \(\pi\): \(288=\frac{4}{3}r^{3}\). Then multiply both sides by \(\frac{3}{4}\): \(r^{3}=288\times\frac{3}{4}=216\).

Step4: Solve for \(r\)

Take the cube - root of both sides: \(r=\sqrt[3]{216}\). Since \(6\times6\times6 = 216\), \(r = 6\).

Answer:

D. 6 cm