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Solid with dimensions in a given ratio and one measure (area or volume) given: find another measure

This type of question, asked 3 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 26 Oct 2023 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    69
    The radius and height of a right circular cone are in the ratio 3:43 : 4. If its curved surface area (in cm2\text{cm}^2) is 240π240\pi, then its volume (in cm3\text{cm}^3) is:

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  2. Question 2

    29 Jan 2022 Tier II

    12
    The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is 4838.4π cm34838.4\pi\ \text{cm}^3, then its radius is:

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  3. Question 3

    26 Oct 2023 Tier II

    8
    The ratio of the length, width and height of a closed cuboid is given as 6 : 3 : 2. The total surface area of this cuboid is given as 1800 cm2\text{cm}^2. Find the volume (in cm3\text{cm}^3) of this cuboid.

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