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Ratio of volumes of two cones or cylinders from ratios of radii and heights

This type of question, asked 3 times: CDS 2 2018, CDS 1 2019, CDS 2 2020. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    86
    Two cones have their heights in the ratio 1:31 : 3. If the radii of their bases are in the ratio 3:13 : 1, then the ratio of their volumes will be

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  2. Question 2

    CDS 1 2019

    49
    Two cylinders of equal volume have their heights in the ratio 2:32 : 3. What is the ratio of their radii ?

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  3. Question 3

    CDS 2 2020

    77
    The volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. What is the ratio of their heights ?

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