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.
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
56A 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 ?Tap an option to check your answer.
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
58A 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 ?Tap an option to check your answer.
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.51What is the whole surface area of the frustum ?Tap an option to check your answer.
52What is the volume of the frustum ?Tap an option to check your answer.
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
52A 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 ?Tap an option to check your answer.
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
76A 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 ?Tap an option to check your answer.
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
77A conical tent has an angle of at the vertex. If the curved surface area is m, then what is the volume of the tent?Tap an option to check your answer.
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
65Three 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 ?Tap an option to check your answer.
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
86A 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 )Tap an option to check your answer.
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
58The 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 ?Tap an option to check your answer.
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
72How many silver coins, 3.5 cm in diameter and of thickness 4 mm, must be melted to form a cuboid of dimensions 21 cm 11 cm 7 cm ? (take )Tap an option to check your answer.