Two cones have the same volume and their base-radii are in the ratio 4 : 5. What is the ratio of their heights?

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Solution

Let the base-radius of the first and the second cone be 4x and 5x respectively.

Let the height of the first and the second cone be h₁and h₂respectively.

Volume of the first cone =

Volume of the second cone

According to the given condition:

Volume of the first cone = Volume of the second cone

Therefore, the ratios of their heights is 25:16.

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