Question

The volumes of two similar cones are 36π cm3 and 288π cm3. The base radius of the smaller cone is 3 cm.  Calculate the base radius of the larger cone.

Answer 1

`V_1=36\pi\ cm^3\\\\V_2=288\pi\ cm^3\\\\(V_2)/(V_1)=k^3\ \ \ (k-similar\ scale)\\\\k^3=(288\pi)/(36\pi)\\\\k^3=8\\\\k=\sqrt[3]8\\\\k=2`


`the\ base\ radius\ of\ the\ smaller\ cone\ is\ 3cm\\\\the\ base\ radius\ of\ the\ bigger\ cone\ i\ 2\cdot3cm=6cm`