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

Question

if the radius and the height both 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 and height of both the glass cylinder and glass cone are doubled, then we can calculate the new volumes using the formulas for the volume of a cylinder and cone:

For a cylinder:
V1 = π(r^2)(h)
V2 = π((2r)^2)(2h) = 4π(r^2)(h)
V2 = 4V1

For a cone:
V1 = (1/3)π(r^2)(h)
V2 = (1/3)π((2r)^2)(2h) = (1/3)4π(r^2)(h)
V2 = 4V1

Therefore, the volumes of both the glass cylinder and glass cone would increase 4 times if the radius and height were both doubled.