Question

1. a sphere has a volume of 288π cm³. what is the radius of the sphere?

a. 4 cm
b. 5 cm
c. 6 cm
d. 8 cm

Explanation:

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

Step3: Simplify the equation

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: \(r=\sqrt[3]{216}=6\).

Answer:

C. 6 cm