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Melt or pour one solid into identical smaller solids: how many

This type of question, asked 3 times: 8 Aug 2022 Tier II, 3 Mar 2023 Tier II, 26 Oct 2023 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    8 Aug 2022 Tier II

    95
    The radius of a solid sphere is 42 cm. It is melted to form identical small solid spheres whose radius is 7 cm. What is the number of small solid spheres obtained?

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  2. Question 2

    3 Mar 2023 Tier II

    20
    A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

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  3. Question 3

    26 Oct 2023 Tier II

    17
    A solid cube, whose each edge is of length 48 cm, is melted. Identical solid cubes, each of volume 64 cm3\text{cm}^3, are made out of this molten cube, without any wastage. How many such small cubes are obtained?

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