Question 56

if the ratio of the volumes of two right circular 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 heights of the two cones respectively be $$h_1$$ and $$h_2$$

Let their radii be $$r$$ and $$2r$$ respectively.

Thus, volume of cone = $$\frac{1}{3} \pi r^2h$$

According to ques, => $$\frac{\frac{1}{3}\pi r^2h_1}{\frac{1}{3}\pi (2r)^2h_2}=\frac{2}{3}$$

=> $$\frac{h_1}{4h_2}=\frac{2}{3}$$

=> $$\frac{h_1}{h_2}=\frac{8}{3}$$

=> Ans - (B)

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