PYQ Vault

Largest sphere inside a cube or box: empty space or sphere surface area

This type of question, asked 5 times: 18 Sep 2025 S2, 19 Sep 2025 S1, 23 Sep 2025 S1, 23 Sep 2025 S3, 24 Sep 2025 S1. All 5 questions below, oldest first.

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  1. Question 1

    18 Sep 2025 S2

    60
    A marble is spherical in shape with a radius of 4 cm. If the marble is placed inside a cube with side length 10 cm, what is the volume of the cube that is not occupied by the marble?

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  2. Question 2

    19 Sep 2025 S1

    61
    A solid sphere is placed inside a cube such that it touches all six faces. What percentage of the cube's volume is not occupied by the sphere?

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  3. Question 3

    23 Sep 2025 S1

    54
    A sphere is inscribed inside a cube. The volume of the cube is 1728 cm3\text{cm}^3. What is the total surface area of the sphere?

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  4. Question 4

    23 Sep 2025 S3

    55
    A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?

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  5. Question 5

    24 Sep 2025 S1

    55
    A rectangular tank measures 12 cm long, 10 cm wide, and 6 cm high. If a spherical ball of the largest possible size is placed inside this tank, what is the volume of the space not occupied by the ball?

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