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.How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
2. 2.An open cylindrical vessel of internal diameter $7\mathrm{cm}$ and height $8\mathrm{cm}$ stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is $3.5\mathrm{cm}$ and height $8\mathrm{cm}$, as shown in the diagram: . When the vessel is filled with water, which labelled part of the diagram represents the volume of water required to fill the vessel?
   • A.The entire internal volume of the cylinder
   • B.The volume of the cylinder not occupied by the cone
   • C.The volume of the cone alone
   • D.The sum of the volumes of the cylinder and the cone
3. 3.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?
4. 4.Two solid spheres of radii $2\mathrm{cm}$ and $4\mathrm{cm}$ are melted and recast into a cone of height $8\mathrm{cm}$. Find the radius of the cone so formed.
5. 5.The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other end. Given that the common radius is 3.5 cm, the height of the cylinder is 6.5 cm, and the total height of the solid is 12.8 cm, which labeled part of the solid corresponds to the height calculation of 2.8 cm?
   • A.The height of the cone
   • B.The height of the hemisphere
   • C.The combined height of the cylinder and cone
   • D.The radius of the hemisphere