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Sphere recast into n equal smaller spheres: compare surface areas

This type of question, asked 2 times: CDS 1 2023, CDS 2 2026. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2023

    69
    A solid iron ball is melted and 64 smaller solid balls of equal size are made using the entire volume of iron. What is the ratio of the surface area of the larger ball to the sum of the surface areas of all the smaller balls ?

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  2. Question 2

    CDS 2 2026

    77
    A spherical metal ball is molten and made into n smaller identical spheres. In this process, the surface area of the smaller balls increases by 900%. What is the value of n ?

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