CBSE Class 10 Mathematics (Standard) Chapter 12 Surface Areas and Volumes Important Questions 2027
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25 questions from Surface Areas and Volumes appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Mensuration unit — 10 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 3.6 questions per paper (OR alternatives counted separately)
- 4 question patterns repeated across papers
Important topics in Surface Areas and Volumes
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere) | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Volume of combination of solids | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Surface area of combination of solids | Board 2022Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| 4 | Word problems on combined solids | Board 2024 | ★☆☆☆☆ |
Repeated questions from Surface Areas and Volumes
1. Ice-cream volume: cone partly unfilled plus hemisphere top
2×Board 2023Sample 20263/5 marks
An empty cone of radius 3cm and height 12cm is filled with ice-cream such that the lower part of the cone which is (1/6)th of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.
2. Surface area of remaining solid after hollowing
2×Board 2022Sample 20264/5 marks
From a solid right circular cone, whose height is 6cm and radius of base is 12cm, a right circular cylindrical cavity of height 3cm and radius 4cm is hollowed out such that bases of cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of pi.
3. Curved surface area of a cone from radius and height
2×Board 2023Sample 20251 marks
[case context] Silo = cylinder (r 1.5 m, h 7 m) + cone (r 1.5 m, h 2 m) on top. (ii) Find the curved surface area of the conical part of one silo.
4. Room as cylinder plus hemispherical dome given air volume
2×Board 2023Board 20253 marks
A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains 1408/21 m3 of air, find the height of the cylindrical part. (Use pi = 22/7).
Surface Areas and Volumes questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 1 | 4 |
| Board 2023 | 4 | 8 |
| Board 2024 | 3 | 5 |
| Board 2025 | 2 | 4 |
| Sample 2025 | 6 | 8 |
| Board 2026 | 6 | 8 |
| Sample 2026 | 3 | 11 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Surface Areas and Volumes
Board 2026 6 questions
A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in cm3) is : (A) 182 pi (B) (182/3) pi (C) (682/3) pi (D) (364/3) pi
Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm2. Reason (R) : The surface area of a cuboid of dimensions l x b x h is (lb + bh + hl). [Choose: both true R explains A / both true R does not explain A / A true R false / A false R true]
[case context: at a fair, parents buy a Rubik's cube (cube) and a strawberry ice-cream (hemisphere on cone shape)] Find the length of the diagonal of Rubik's cube if each edge measures 6 cm.
[case context: at a fair, parents buy a Rubik's cube (cube) and a strawberry ice-cream (hemisphere on cone shape)] Find the volume of Rubik's cube if the length of the edge is 7 cm.
[case context: at a fair, parents buy a Rubik's cube (cube) and a strawberry ice-cream (hemisphere on cone shape)] What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm ?
[case context: at a fair, parents buy a Rubik's cube (cube) and a strawberry ice-cream (hemisphere on cone shape)] If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.
Sample 2026 3 questions
If the area of the base of a right circular cone is 51 cm2 and its volume is 85 cm3, then the height of the cone is given as (A) 5/6 cm (B) 5/3 cm (C) 5/2 cm (D) 5 cm
From a solid right circular cone, whose height is 6cm and radius of base is 12cm, a right circular cylindrical cavity of height 3cm and radius 4cm is hollowed out such that bases of cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms of pi.
An empty cone of radius 3cm and height 12cm is filled with ice-cream such that the lower part of the cone which is (1/6)th of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.
Board 2025 2 questions
Assertion (A) : If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R) : Total Surface Area of a sphere of radius r is 3*pi*r2. Choose the correct option: (A) Both A and R true, R correct explanation of A (B) Both A and R true, R not correct explanation of A (C) A true, R false (D) A false, R true
A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains 1408/21 m3 of air, find the height of the cylindrical part. (Use pi = 22/7).
Sample 2025 6 questions
The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is A) 5 cm B) 20 cm C) 10 cm D) 4 cm
The volume of a solid hemisphere is 396/7 cm3. The total surface area of the solid hemisphere (in sq.cm) is A) 396/7 B) 594/7 C) 549/7 D) 604/7
[case context] Farmer Girdhar builds a metallic silo shaped as a cylinder (radius 1.5 m, height 7 m) mounted by a cone (base radius 1.5 m, height 2 m). (i) Calculate the slant height of the conical part of one silo.
[case context] Silo = cylinder (r 1.5 m, h 7 m) + cone (r 1.5 m, h 2 m) on top. (ii) Find the curved surface area of the conical part of one silo.
[case context] Silo = cylinder (r 1.5 m, h 7 m) + cone (r 1.5 m, h 2 m) on top. (iii)(A) Find the cost of metal sheet used to make the curved cylindrical part of 1 silo at the rate of Rs 2000 per m2.
[case context] Silo = cylinder (r 1.5 m, h 7 m) + cone (r 1.5 m, h 2 m) on top. (iii)(B) Find the total capacity of one silo to store grains.
Board 2024 3 questions
A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is: (a) 1:1 (b) 1:4 (c) 2:3 (d) 3:2
The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is: (a) 4pi/3 cu cm (b) 5pi/3 cu cm (c) 8pi/3 cu cm (d) 2pi/3 cu cm
The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is 176 cm3, find the outer and inner radii of the cylinder.
Board 2023 4 questions
Curved surface area of a cylinder of height 5 cm is 94.2 cm2. Radius of the cylinder is (Take pi = 3.14) (A) 2 cm (B) 3 cm (C) 2.9 cm (D) 6 cm
The curved surface area of a cone having height 24 cm and radius 7 cm, is (A) 528 cm2 (B) 1056 cm2 (C) 550 cm2 (D) 500 cm2
A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find total height of the room if it contains (1408/21) m3 of air. (Take pi = 22/7)
An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is (1/6)th of the volume of the cone is unfilled but hemisphere is formed on the top. Find volume of the ice-cream. (Take pi = 3.14)
Board 2022 1 question
From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 12 Surface Areas and Volumes?
By how often and how recently they were asked: Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere); Volume of combination of solids; Surface area of combination of solids.
How many marks does Surface Areas and Volumes carry in the CBSE Class 10 Mathematics (Standard) exam?
Surface Areas and Volumes is part of the Mensuration unit, which carries 10 marks in the official syllabus. In the analysed papers it had about 3.6 questions per paper.
Do questions from Surface Areas and Volumes repeat in board exams?
Yes — 4 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.