Question

A cone and a cylinder have the same volume and the same base radius. If you are given only the height of the cylinder, is it possible to figure out the height of the cone? If so, how would you figure it out?

Am thinking yes, because if they are the same in volume then the height must be the same right?

Answer 1

V (Cylinder) = pi * r^2 * h

V (cone) = 1/3 * pi * r^2 * h

Since volumes are = :

pi * r^2 * h = 1/3 * pi * r^2 * h

Since pi and r^2 are the same values, dividing both sides by these terms will cancel them out. What does that tell you about the heights? Are they the same?

I hope this helps.