1. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be
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By: anil on 05 May 2019 01.55 am
Let the radii of two cones be $$r_1 = x$$ and $$r_2 = 2x$$ Let the heights of the two cones be $$h_1$$ and $$h_2$$ => Ratio of volumes : => $$frac{frac{1}{3} pi r_1^2 h_1}{frac{1}{3} pi r_2^2 h_2} = frac{2}{3}$$ => $$frac{x^2 h_1}{4x^2 h_2} = frac{2}{3}$$ => $$frac{h_1}{h_2} = frac{8}{3}$$ => Required ratio = 8 : 3
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