If the volumes of two cones are in the ratio 2 : 3 and the radii of their bases are in the ratio 1 : 2, then the ratio of their heights will be:

8 : 3

Volume of cone = \(\frac{1}{3}\)πr²h

\(\frac{V1}{V2}\) = \(\frac{2}{3}\)

\(\frac{πr²h}{πR²H}\) = \(\frac{2}{3}\)

\(\frac{1²h}{2²H}\) = \(\frac{2}{3}\)

\(\frac{h}{4H}\) = \(\frac{2}{3}\)

\(\frac{h}{H}\) = \(\frac{8}{3}\)

 So, ratio of their heights , h : H = 8 : 3