Question

If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of cylinder r is ________?

Answer 1

Volume of a cylinder with radius r and height H, Vc = π (r^2)*H

Volume of a conce with radius R and height H, Vcone = (1/3) π (R^2) * H

Vcone = Vc => (1/3)π (R^2)*H = π(r^2)*H

=> R^2 = 3 * (r^2)

=> R = r√3

Answer: R = r √3