A right circular cone is sliced into four pieces by planes parallel to its base. All of these pieces have the same height. What is the ratio of the volume of the second-largest piece to the volume of the largest piece? Express your answer as a common fraction.

supremecheetah May 19, 2023

#1**0 **

Let the radius of the cone be r and the height be h. The volume of the cone is 1/3πr^2h. The second-largest piece is a smaller cone with radius r and height 2/3h, so its volume is 13πr^2⋅2/3h=2/9πr^2h. The largest piece is the original cone, so its volume is 1/3πr^2h. Therefore, the ratio of the volume of the second-largest piece to the volume of the largest piece is 2/9.

Guest May 19, 2023