Question 484652
Instead of using all these variables (V1, V, R1, R, h, h1), just use V, V1, r, and h. The volume of the original cone is


*[tex \LARGE V = \frac{1}{3}\pi r^2 h]


and the volume of the new cone is


*[tex \LARGE V_1 = \frac{1}{3}\pi (2r)^2 \frac{h}{3}]


*[tex \LARGE = \frac{1}{3} \pi 4r^2 \frac{h}{3} = \frac{4}{3} (\frac{1}{3} \pi r^2 h) = \frac{4}{3}V]


Hence the ratio of the new volume to the original volume is (4/3)V : V, or 4/3:1   = 4:3.