Surface Areas and Volumes

CBSE Class 10 · Mathematics · 26 past questions

These are the board's own papers. 81 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026

A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m$^2$. Outer surface…
Q2 2026

An ice-cream cone of radius r and height h is completely filled by two spherical scoops of ice-cream. If…
Q3 2026

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed… (with a figure)
Q4 2026 (Basic)

‘Gilli Danda’ is a very popular traditional game of India which is played with two wooden sticks – the larger… (with a figure)
Q5 Sample paper 2026-27

Two cubes each of volume 64 cm³ are joined end to end to form a solid. The surface area of the resultant…
Q6 Sample paper 2026-27

A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical…
Q7 2025

If the volumes of two cubes are in the ratio 8 : 125, then the ratio of their surface areas is…
Q8 2025

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is…
Q9 2025

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…
Q10 2025

A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is…
Q11 2025 (Basic)

A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The…
Q12 2024

The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts… (with a figure)
Q13 2024

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two…
Q14 2024

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is…
Q15 2024

The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm.…
Q16 2024 (Basic)

The radius of a sphere is $\frac{7}{2}$ cm. The volume of the sphere is…
Q17 2024 (Basic)

The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone…
Q18 2024 (Basic)

A solid is in the form of a cylinder with hemi–spherical ends of same radii. The total height of the solid is…
Q19 2023

What is the total surface area of a solid hemisphere of diameter ‘d’ ?
Q20 2023

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and… (with a figure)
Q21 2023

A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a…
Q22 2023

Curved surface area of a cylinder of height 5 cm is 94.2 cm². Radius of the cylinder is (Take $\pi$ = 3.14)
Q23 2023

The curved surface area of a cone having height 24 cm and radius 7 cm, is
Q24 2023 (Basic)

The volume of a cone of radius 'r' and height '3r' is…
Q25 2023 (Basic)

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The…
Q26 2022 (Basic)

A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm in radius. The radius of the spherical…