one glass cylinder and one glass cone with the same height and radius

Question

if the radius of the glass doubled and then the volumes would increase times ___
(use for formulas to substitute V=1/3πr^2h and V=πr^2h)

Answer 1

If the radius of the glass is doubled, the new radius will be twice the original radius, so r' = 2r.

For the cone:
V' = 1/3 * π * (2r)^2 * h = 1/3 * π * 4r^2 * h = 4/3 * π * r^2 * h

For the cylinder:
V' = π * (2r)^2 * h = π * 4r^2 * h = 4 * π * r^2 * h

Therefore, the volumes would increase by a factor of 4.