What effect does doubling the radius and tripling the height of a cone have on the cone's volume?

The volume of a cone is given by the formula ( V = \frac{1}{3} \pi r^2 h ). If the radius is doubled (from ( r ) to ( 2r )) and the height is tripled (from ( h ) to ( 3h )), the new volume becomes ( V' = \frac{1}{3} \pi (2r)^2 (3h) = \frac{1}{3} \pi (4r^2)(3h) = 4 \pi r^2 h ). This means the new volume is four times the original volume, so the effect of these changes is that the volume of the cone increases by a factor of 4.