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How many small solids fill or come from a big one: divide the volumes

This type of question, asked 4 times: CDS 2 2016, CDS 1 2017, CDS 2 2020, CDS 2 2021. All 6 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    45
    Into a conical tent of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be emptied, if space required for the wheat in each bag is 1.96 m31.96\ \text{m}^3 ?

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  2. Question 2

    CDS 1 2017

    87
    Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is

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  3. Question 3

    CDS 2 2020

    74
    The length, breadth and height of a brick are 20 cm, 15 cm and 10 cm respectively. The number of bricks required to construct a wall with dimensions 45 m length, 0.15 m breadth and 3 m height is

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  4. Question 4

    CDS 2 2020

    67
    How many solid lead balls each of diameter 2 mm can be made from a solid lead ball of radius 8 cm ?

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  5. Question 5

    CDS 2 2021

    72
    How many silver coins, 3.5 cm in diameter and of thickness 4 mm, must be melted to form a cuboid of dimensions 21 cm ×\times 11 cm ×\times 7 cm ? (take π=227\pi = \frac{22}{7})

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  6. Question 6

    CDS 2 2021

    67
    A hemispherical bowl of internal radius 18 cm contains a liquid. The liquid is filled in small cylindrical bottles of internal radius 3 cm and internal height 4 cm. What is the number of bottles used to empty the bowl ?

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