If the volume of a sphere is 756 cubic cm, what is the radius in cm?

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

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

Here, ( V ) is the volume and ( r ) is the radius. In this case, we have the volume ( V = 756 ) cubic cm.

First, we can rearrange the formula to solve for the radius ( r ):

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

Substituting the given volume into the equation:

[ r^3 = \frac{3 \times 756}{4\pi} ]

Calculate ( 3 \times 756 ) to get 2268, and then divide by ( 4\pi ):

[ r^3 = \frac{2268}{4\pi} ]

Now, approximate ( \pi ) as about 3.14:

[ r^3 \approx \frac{2268}{12.56} \approx 180 ]

Now take the cube root to find ( r ):

[ r \approx \sqrt[3]{180} \approx