### Video Transcript

The volume of a cone is 441π cubic centimeters, and its height is 12 centimeters. Find its diameter.

For some cone with the volume of 441π cubic centimeters and a height of 12 centimeters, we want to know the diameter. Recall that the volume of any cone is equal to one-third π times the radius squared times the height. We know the volume and the height, which means we can first solve for the radius and then find the diameter. In this case, weβll have 441π equals one-third π π squared times 12. One-third times 12 equals four, which means 441π is equal to four π π squared. If we divide through by π, the π term on either side of the equation is canceled. So 441 equals four π squared, and π squared equals 441 over four. This means the radius will be equal to the square root of 441 over four.

Itβs worth noting here that we only need the positive square root since weβre dealing with distance. Both 441 and four are squares, which means we can take the square root of the numerator and the square root of the denominator. The radius is therefore equal to 21 over two. The diameter is equal to two times the radius. Two times 21 over two equals 21. And weβre working in centimeters.

The diameter of a cone with the volume of 441π cubic centimeters and a height of 12 centimeters would be 21 centimeters.