if the radius and the height both doubled then the volume would icrease times ___
(use for formulas to substitute V=1/3πr^2h and V=πr^2h)
If the radius and height are both doubled, the new volume would increase by a factor of 8.
Using V=1/3πr^2h:
The original volume is V=1/3πr^2h
The new volume is V'=1/3π(2r)^2(2h) = 1/3π(4r^2)(2h)
The new volume is V' = 8(1/3πr^2h) = 8V
Using V=πr^2h:
The original volume is V=πr^2h
The new volume is V'=π(2r)^2(2h) = π(4r^2)(2h)
The new volume is V' = 8(πr^2h) = 8V
Therefore, if the radius and height are both doubled, the volume would increase by a factor of 8.