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Two solids with equal volumes (and equal radii): ratio or value of a dimension

This type of question, asked 5 times: 18 Jul 2023 S4, 13 Sep 2025 S3, 15 Sep 2025 S1, 16 Sep 2025 S1, 17 Sep 2025 S3. All 5 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S4

    65
    A cone and a cylinder with equal radii have equal volumes. The ratio of their heights is :

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  2. Question 2

    13 Sep 2025 S3

    70
    A cone and a hemisphere have the same volume and base radius. Find the ratio of the height of the cone to its radius.

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  3. Question 3

    15 Sep 2025 S1

    66
    A cylinder and hemisphere have the same radius. Their combined height is 30 cm. If the cylinder and hemisphere have equal volumes, find the radius.

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  4. Question 4

    16 Sep 2025 S1

    65
    A hemisphere and a cone share the same base and have equal volumes. Given that their common radius is R, determine the height of the cone.

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  5. Question 5

    17 Sep 2025 S3

    60
    A cone and a sphere have equal volumes. If the cone's height is twice its radius, what is the ratio of the cone's radius to the sphere's radius?

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