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 what?

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 what?

Answer 1

volume of a cone = (1/3)pir²h = volume of a cylinder =pir²h

r=radius of the cone

R=radius of the cylinder

pi and h cancel leaving

(1/3)r² = R²

take the square root of both sides

(1/3)^1/2 r = R

R= about 0.577r

or

r=R/(1/3)^1/2=1.732R = 3^1/2R = R times square root of 3

radius of the cone = square root of 3 times the radius of the cylinder