Question

the formula for the volume of a cylinder is v = πr2h. the volume of a cylinder is three times the volume of a cone with the same radius and height. 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

Let R be radius of cylinder and r the radius of cone.
πR^2h = 1/3πr^2h
R^2 = 1/3r^2
r^2 = 3R^2
r = sqrt(3) x R