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Question 141
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
Solution
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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