If a sphere has a volume of 288π cubic cm, what is its radius?

To find the radius of a sphere given its volume, we use the formula for the volume of a sphere, which is:

[ V = \frac{4}{3} \pi r^3 ]

where ( V ) is the volume and ( r ) is the radius. In this case, we're given that the volume ( V = 288\pi ) cubic cm.

To find the radius, we can set up the equation:

[ 288\pi = \frac{4}{3} \pi r^3 ]

We can eliminate ( \pi ) from both sides of the equation, resulting in:

[ 288 = \frac{4}{3} r^3 ]

Next, we will isolate ( r^3 ) by multiplying both sides by ( \frac{3}{4} ):

[ r^3 = 288 \times \frac{3}{4} ]

Calculating that gives:

[ r^3 = 288 \times 0.75 = 216 ]

Now to find ( r ), we take the cube root of 216:

[ r = \sqrt[3]{216} = 6 , \text{cm}