ICSE Class 10

ICSE Class 10 Surface Area and Volume (Cylinder, Cone, Sphere) — Mock Test (2027)

Free online mock test for Surface Area and Volume (Cylinder, Cone, Sphere) (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

What to expect: This mock test covers key concepts from the Surface Area and Volume (Cylinder, Cone, Sphere) chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.

Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.

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Sample questions

  1. 1.A solid, consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water, and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of cone is 4 cm. Give your answer to the nearest cubic centimetre.
  2. 2.An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 3.5 cm and height 8 cm. The volume of water required to fill the vessel is first calculated. If this cone is then replaced by another cone, whose height is 1.75 cm and the radius of whose base is 2 cm, what is the drop in the water level?
    • A.0.5 cm
    • B.1.5 cm
    • C.2.0 cm
    • D.3.0 cm
  3. 3.The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.
  4. 4.In the given diagram, there is water to a height of 16 cm in a cylindrical glass jar of radius 12.5 cm. Inside the water, a sphere of diameter 15 cm is completely immersed. img-1.jpeg By what height will the water level go down when the sphere is removed?
    • A.2.4 cm
    • B.3.6 cm
    • C.4.8 cm
    • D.6.0 cm
  5. 5.A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0·5 cm. How many spheres are formed?
    • A.80
    • B.160
    • C.200
    • D.400

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