there is a glass cylinder and a glass cone with the same height and radius

Question

If the radius of the glasses doubled, then the volumes would increase times ___

Answer 1

The volume of a cylinder is calculated using the formula V = πr^2h and the volume of a cone is calculated using the formula V = (1/3)πr^2h.

If the radius of both the cylinder and the cone is doubled, the new volume of the cylinder would be V' = π(2r)^2h = 4πr^2h = 4V, and the new volume of the cone would be V' = (1/3)π(2r)^2h = (4/3)πr^2h = 4/3V.

Therefore, the volume of the cylinder would increase by a factor of 4 times, and the volume of the cone would increase by a factor of 4/3 times.