PYQ Vault

Longest diagonal of a cube or cuboid (longest stick), or volume from it

This type of question, asked 3 times: 25 Jul 2023 S4, 17 Sep 2024 S3, 23 Sep 2024 S1. All 3 questions below, oldest first.

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  1. Question 1

    25 Jul 2023 S4

    51
    The length of the longest diagonal of a cube is 737\sqrt{3} cm. Find its volume (in cm3\text{cm}^3).

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  2. Question 2

    17 Sep 2024 S3

    56
    Find the length of the longest diagonal (in cm) of a cuboidal box of dimensions 1.2 cm ×\times 1.3 cm ×\times 1.5 cm (correct to two decimal places).

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  3. Question 3

    23 Sep 2024 S1

    67
    Find the length of the longest stick that can be fitted in a cubical vessel of edge 70 cm.

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