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

$V_1=36\pi\ cm^3\\\\V_2=288\pi\ cm^3\\\\\frac{V_2}{V_1}=k^3\ \ \ (k-similar\ scale)\\\\k^3=\frac{288\pi}{36\pi}\\\\k^3=8\\\\k=\sqrt[3]8\\\\k=2$

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