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.

Sample questions

1. 1.Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2\,\mathrm{cm}$ and height $16\,\mathrm{cm}$. The diameter of each sphere is
   • a.$4\,\mathrm{cm}$
   • b.$3\,\mathrm{cm}$
   • c.$2\,\mathrm{cm}$
   • d.$6\,\mathrm{cm}$
2. 2.A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly around it to a width of 5 m to form an embankment. Find the height of the embankment.
3. 3.A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with the hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm³, will be required to fill the vessel completely?
   • A.1078 cm³
   • B.1127 cm³
   • C.980 cm³
   • D.1232 cm³
4. 4.A cone is $40\mathrm{cm}$ high. A small cone is cut off at the top by a plane parallel to its base. If its volume be $\frac{1}{64}$ of the volume of the given cone, at what height above the base is the section cut?
5. 5.A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
   • A.7 cm
   • B.14 cm
   • C.21 cm
   • D.28 cm