Answer to Question #4213 in Geometry for Bridgette

Question

A cone has a radius of r units and a height of h units. A cylinder has a radius of 2r units and has the same volume as the cone. WHat is the height of the cylinder?

Answer 1

The volume of the cone is equal to
V = 1/3 π r² h
The volume of the cylinder is
V = π (2r)² H
Thus
1/3 π r² h = π 4r² H
1/3 h = 4 H
H = 1/12 h