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Several spheres or cubes melted into one (or one into several): sum of cubes of radii or edges is conserved

This type of question, asked 4 times: CDS 1 2019, CDS 1 2021, CDS 1 2022, CDS 2 2023. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2019

    66
    Three copper spheres of radii 3 cm, 4 cm and 5 cm are melted to form a large sphere. What is its radius ?

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  2. Question 2

    CDS 1 2021

    65
    A metal solid cube of edge 24 cm is melted and made into three small cubes. If the edges of two small cubes are 12 cm and 16 cm, then what is the surface area of the third small cube?

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  3. Question 3

    CDS 1 2022

    66
    A spherical ball of lead 6 cm in diameter is melted and recast into three spherical balls. The diameters of the balls are 2 cm, 4 cm and xx cm. Which one of the following is correct?

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  4. Question 4

    CDS 2 2023

    65
    Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface areas of the three spheres ?

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