PYQ Vault

Mensuration 3D

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 5 times: CDS 1 2019, CDS 1 2021, CDS 2 2023, CDS 1 2024, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    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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  2. Question 2

    This type asked 5 times: CDS 2 2017, CDS 1 2021, CDS 1 2022, CDS 2 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    58
    A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise ?

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  3. Question 3 (case study, 2 parts)

    This type asked 5 times: CDS 2 2016, CDS 1 2019, CDS 2 2020, CDS 2 2021, CDS 1 2025. This one: CDS 1 2025 See all 5 of this type

    Consider the following for the next two (02) items that follow : A frustum of a right cone has a top of diameter 2k, bottom of diameter 2.5k and height k.
    51
    What is the whole surface area of the frustum ?

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    52
    What is the volume of the frustum ?

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  4. Question 4

    This type asked 5 times: CDS 2 2016, CDS 2 2017, CDS 1 2018, CDS 2 2022, CDS 2 2023. This one: CDS 2 2023 See all 5 of this type

    52
    A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circumferences are respectively 30 cm and 40 cm. The perpendicular distance between the ends is 6 cm. If the cone were to be completed, then how far would its vertex be from the top end ?

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  5. Question 5

    This type asked 4 times: CDS 2 2021, CDS 2 2022, CDS 1 2025, CDS 2 2026. This one: CDS 2 2026 See all 4 of this type

    76
    A room is L m long, B m wide and H m high. Further, L > B > H and L, B and H are integers. The length of the longest pole that can be placed in the room is 17 m and the length of the longest pole that can be placed on the floor is 15 m. What is the volume of the room ?

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  6. Question 6

    This type asked 4 times: CDS 2 2017, CDS 2 2024, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    77
    A conical tent has an angle of 60∘60^\circ at the vertex. If the curved surface area is 100100 m2^2, then what is the volume of the tent?

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  7. Question 7

    This type asked 4 times: CDS 1 2019, CDS 1 2021, CDS 1 2022, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    65
    Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface areas of the three spheres ?

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  8. Question 8

    This type asked 4 times: CDS 2 2017, CDS 1 2021, CDS 1 2022, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    86
    A square sheet of side length 44 cm is rolled along one of its sides to form a cylinder by making opposite edges just to touch each other. What is the volume of the cylinder ? (Take π=227\pi = \frac{22}{7})

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  9. Question 9

    This type asked 4 times: CDS 1 2017, CDS 2 2019, CDS 2 2020, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    58
    The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is correct ?

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  10. Question 10

    This type asked 4 times: CDS 2 2016, CDS 1 2017, CDS 2 2020, CDS 2 2021. This one: CDS 2 2021 See all 4 of this type

    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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