CBSE Class 10 Mathematics (Basic) Chapter 12 Surface Areas and Volumes Important Questions 2027
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20 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 2.9 questions per paper (OR alternatives counted separately)
- 6 question patterns repeated across papers
Important topics in Surface Areas and Volumes
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Surface area of combination of solids | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| 2 | Volume of combination of solids | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| 3 | Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere) | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
Repeated questions from Surface Areas and Volumes
1. Surface area of a combined solid
3×Board 2022Board 2024Sample 20252/3/4 marks
[Case study: A jumbo pencil, when sharpened, is a combination of a cylinder and a cone. Length of the cylindrical portion is 21 cm, diameter of the base is 1 cm, and height of the conical portion is 1.2 cm.] Find the total surface area of the pencil (in terms of π).
2. Solid with CSA equal to TSA
2×Board 2025Board 20261 marks
For which of the following solids is the lateral/curved surface area and total surface area the same ? (A) Cube (B) Cuboid (C) Hemisphere (D) Sphere
3. Volume of a cone-on-hemisphere toy
2×Board 2025Board 20265 marks
A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The height of the conical part of the toy is equal to the diameter of its base. If the radius of the conical part is 5 cm, find the volume of the toy.
4. Cube surmounted by a hemisphere: edge + TSA
2×Board 2025Board 20265 marks
A cubical block is surmounted by a hemisphere of radius 3.5 cm. What is the smallest possible length of the edge of the cube so that the hemisphere can totally lie on the cube ? Find the total surface area of the solid so formed.
5. Volume of a standard solid
2×Board 2023Board 20241 marks
The radius of a sphere is 7/2 cm. The volume of the sphere is : (a) 231/3 cu cm (b) 539/12 cu cm (c) 539/3 cu cm (d) 154 cu cm
6. Capacity of a vessel (cylinder + sphere/hemisphere)
2×Board 2022Board 20243/4 marks
A juice glass is cylindrical in shape with hemi-spherical raised up portion at the bottom. The inner diameter of glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use π = 3.14)
Surface Areas and Volumes questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 2 | 8 |
| Board 2023 | 2 | 6 |
| Board 2024 | 4 | 8 |
| Board 2025 | 3 | 11 |
| Sample 2025 | 5 | 7 |
| Board 2026 | 3 | 11 |
| Sample 2026 | 1 | 5 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Surface Areas and Volumes
Board 2026 3 questions
For which of the following solids is the lateral/curved surface area and total surface area the same ? (A) Cube (B) Cuboid (C) Hemisphere (D) Sphere
A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The height of the conical part of the toy is equal to the diameter of its base. If the radius of the conical part is 5 cm, find the volume of the toy.
A cubical block is surmounted by a hemisphere of radius 3.5 cm. What is the smallest possible length of the edge of the cube so that the hemisphere can totally lie on the cube ? Find the total surface area of the solid so formed.
Sample 2026 1 question
A solid toy is in the form of a hemisphere surmounted by a right circular cone of height 2 cm and diameter of base 4 cm. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. [Use π = 3.14]
Board 2025 3 questions
For which of the following solids is the lateral/curved surface area and total surface area the same ? (A) Cube (B) Cuboid (C) Hemisphere (D) Sphere
A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The height of the conical part of the toy is equal to the diameter of its base. If the radius of the conical part is 5 cm, find the volume of the toy.
A cubical block is surmounted by a hemisphere of radius 3.5 cm. What is the smallest possible length of the edge of the cube so that the hemisphere can totally lie on the cube ? Find the total surface area of the solid so formed.
Sample 2025 5 questions
The total surface area of solid hemisphere of radius r is (A) πr2 (B) 2πr2 (C) 3πr2 (D) 4πr2
[Case study: A jumbo pencil, when sharpened, is a combination of a cylinder and a cone. Length of the cylindrical portion is 21 cm, diameter of the base is 1 cm, and height of the conical portion is 1.2 cm.] Find the slant height of the sharpened part.
[Case study: A jumbo pencil, when sharpened, is a combination of a cylinder and a cone. Length of the cylindrical portion is 21 cm, diameter of the base is 1 cm, and height of the conical portion is 1.2 cm.] Find curved surface area of sharpened part (in terms of π).
[Case study: A jumbo pencil, when sharpened, is a combination of a cylinder and a cone. Length of the cylindrical portion is 21 cm, diameter of the base is 1 cm, and height of the conical portion is 1.2 cm.] Find the total surface area of the pencil (in terms of π).
[Case study: A jumbo pencil, when sharpened, is a combination of a cylinder and a cone. Length of the cylindrical portion is 21 cm, diameter of the base is 1 cm, and height of the conical portion is 1.2 cm.] The pencil's total height decreases by 8.2 cm after sharpening it many times, what is the volume of the cylindrical part of the shortened pencil (in terms of π)?
Board 2024 4 questions
The radius of a sphere is 7/2 cm. The volume of the sphere is : (a) 231/3 cu cm (b) 539/12 cu cm (c) 539/3 cu cm (d) 154 cu cm
The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is : (a) 24 cm (b) 31 cm (c) 26 cm (d) 25 cm
A solid is in the form of a cylinder with hemi-spherical ends of same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.
A juice glass is cylindrical in shape with hemi-spherical raised up portion at the bottom. The inner diameter of glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use π = 3.14)
Board 2023 2 questions
The volume of a cone of radius 'r' and height '3r' is : (a) 1/3 πr3 (b) 3 πr3 (c) 9 πr3 (d) πr3
A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Also, find the volume of the vessel.
Board 2022 2 questions
A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm in radius. The radius of the spherical part is 9 cm. Find the amount of water (in litres) it can hold, when filled completely.
From a solid cylinder, whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter 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 (Basic) Chapter 12 Surface Areas and Volumes?
By how often and how recently they were asked: Surface area of combination of solids; Volume of combination of solids; Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere).
How many marks does Surface Areas and Volumes carry in the CBSE Class 10 Mathematics (Basic) 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 2.9 questions per paper.
Do questions from Surface Areas and Volumes repeat in board exams?
Yes — 6 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.