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Melt or empty one solid into n smaller identical ones: how many

This type of question, asked 3 times: 15 Sep 2025 S1, 19 Sep 2025 S3, 23 Sep 2025 S3. All 3 questions below, oldest first.

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  1. Question 1

    15 Sep 2025 S1

    65
    How many hemispheres with a radius of 3 cm can be produced by melting down a hemisphere with a radius of 12 cm?

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  2. Question 2

    19 Sep 2025 S3

    63
    A solid hemisphere of radius R is melted and recast into n smaller hemispheres of radius r. Find the value of n.

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  3. Question 3

    23 Sep 2025 S3

    54
    A spherical tank is filled with water. The radius of the sphere is 6 meters. The tank is used to fill cylindrical containers, each with a radius of 1 meter and a height of 12 meters. How many containers can be filled?

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