The ratio of the base-radii of two cones is 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?

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Solution

Let the base-radius of the first and the second cone be 3x units and 5x units respectively.

Let the height of the first and the second cone be 2y units and 3y units respectively.

Volume of the first cone =

Volume of the second cone

Ratio of the volumes =

Therefore, the ratio of the volume of the first cone to the second cone is 6:25.

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