right cone

[Nekkamath]

A right cone has a base with a circumference of 16pi inches and a height of 30 inches. The height of this cone is reduced while the circumference stays the same. The volume of the shorter cone is 192pi cubic inches. What is the ratio of the shorter height to the original height? Express your answer as a common fraction.

 

[wjm11]

Cone volume = (1/3)pi*r^2*h

You know the first cone height is 30. Solve for the second cone height.

Then divide your answer by 30. That's "the ratio of the shorter height to the original height."