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Solid or liquid recast into one solid of another shape: find a missing dimension

This type of question, asked 5 times: CDS 1 2019, CDS 1 2021, CDS 2 2023, CDS 1 2024, CDS 2 2026. All 6 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2019

    61
    A hollow sphere of external and internal diameters 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm. What is the height of the cone ?

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  2. Question 2

    CDS 1 2021

    67
    A metal solid cube of side 22 cm is melted to make a cone of height 21 cm. What is the radius of the base of the cone? (Take π=227\pi = \frac{22}{7})

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  3. Question 3

    CDS 1 2021

    66
    A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. What is the height to which the water rises?

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  4. Question 4

    CDS 2 2023

    66
    A solid sphere of radius 3 cm is melted to form a hollow cylinder of height 4 cm and external diameter 10 cm. What is the thickness of the cylinder ?

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  5. Question 5

    CDS 1 2024

    38
    From a circular metal plate of radius 7 cm and thickness 0.16 mm, a sector is cut off containing an angle 150∘150^\circ. The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm ?

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  6. Question 6

    CDS 2 2026

    56
    A well is dug with a diameter of 3.5 m and 16 m depth. The earth soil so excavated is spread in the form of a right circular cone of radius 7 m. What is the height of the cone ?

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