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Solids melted into one or one into several of different sizes: sum of cubes of radii or sides

This type of question, asked 7 times: 17 Jul 2023 S4, 20 Jul 2023 S1, 21 Jul 2023 S3, 25 Jul 2023 S1, 18 Sep 2025 S1, 18 Sep 2025 S2, 20 Sep 2025 S1. All 7 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S4

    66
    A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are 32\frac{3}{2} cm and 2 cm, respectively. Find the diameter of the third ball.

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  2. Question 2

    20 Jul 2023 S1

    74
    Three cubes with sides in the ratio of 3:4:53 : 4 : 5 are melted to form a single cube whose diagonal is 18318\sqrt{3} cm. The sides of the three cubes are:

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  3. Question 3

    21 Jul 2023 S3

    66
    Three solid metallic spheres of radii 1 cm, 6 cm and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere so formed is:

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  4. Question 4

    25 Jul 2023 S1

    54
    A metallic cube has each of its side of length 12 cm. It is melted and recast into three small cubes. Out of these cubes, two have their sides as 6 cm and 8 cm, respectively. The length of each side of the third cube is:

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  5. Question 5

    18 Sep 2025 S1

    62
    Two identical solid hemispheres, each with a radius of 21 cm, are melted and recast into a single sphere. What is the radius of the new sphere formed?

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  6. Question 6

    18 Sep 2025 S2

    61
    Two hemispheres of radii 2 cm and 4 cm respectively are melted and recast into another hemisphere. What is the approximate total surface area of the newly formed hemisphere?

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  7. Question 7

    20 Sep 2025 S1

    57
    Three metallic spheres with radii 3 cm,4 cm, and 5 cm respectively are melted together and recast into a single solid sphere. What is the radius of the new sphere?

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