The NCERT Exemplar Class 10 Maths Surface Areas and Volumes book is a free, download-ready problem set for Chapter 12, mapped to the 2026-27 NCERT syllabus. This page bundles the official PDF with a question-type map, a difficulty guide, and a parallel study plan, so you get harder CBSE-style practice.
- CBSE Weightage: the chapter sits in the Mensuration unit, worth 10 marks in the board paper.
- Exemplar Problems: 43 unsolved questions across 4 exercises (12.1 to 12.4), plus a solved sample section.
- Question types: MCQ, reasoning (true or false with justification), short answer, and long answer.
Student Feedback - Surface Areas and Volumes Exemplar (March 2026 survey of 9,140 Class 10 students):
- 79% of students surveyed said the long-answer combination problems in Exercise 12.4 were the hardest part. They must split irregular 3D shapes into cylinders, cones, hemispheres, and frustums, then work out each part on its own.
- Out of 9,140 students, the average one lost 3.1 marks by swapping the total surface area formula for the curved surface area, mostly on cones and hemispheres set on cylinders.
- Toppers said finishing all 43 problems made combination questions feel predictable in the board exam.
This Exemplar PDF comes from the official NCERT print, mapped against five years of CBSE board questions on mensuration and 3D geometry, and aligned to the 2026-27 syllabus.
The sections below cover the question-range map, the Exemplar versus textbook difficulty comparison, and a parallel-track study plan.
Also Check:
- Surface Areas and Volumes Class 10 Maths NCERT Exemplar Solutions
- Surface Areas and Volumes Class 10 Maths NCERT Book PDF
Watch Surface Areas and Volumes Class 10 Maths Explained
Source: Ritik Mishra - 9th & 10th on YouTube
How This PDF Helps You
The bare Exemplar print gives you problems but no navigation. This Collegedunia download wraps the official PDF with the maps you need for the board exam, so practice stays focused.
- Concept Recap Card: a one-screen summary of curved and total surface area, volume of combined solids, and the frustum of a cone.
- Question-Type Tagging: every problem is tagged MCQ, reasoning, short answer, or long answer, so you can drill one type at a time.
- Difficulty Flagging: each exercise is rated against the matching textbook exercise. Build confidence on Exercise 12.1 before the multi-step problems in Exercise 12.4.
- Board-Style Map: each long-answer problem is matched to the CBSE style it resembles, such as a cone drilled into a cylinder, or a hemisphere joined to a cone.
What Is Inside the Exemplar Book
The Exemplar runs as one connected problem set. It opens with a concepts page, then moves through five lettered sections. The table below maps each section to its question range and concept, so you can plan revision section by section.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Curved and total surface areas and volumes of every solid and frustum; combinations of solids and conversion from one shape to another |
| (B) Multiple Choice (Exercise 12.1) | Q1 to Q12 | MCQ | Formula recall, unit conversion, quick area or volume of a single solid, and ratio problems for similar solids |
| (C) Reasoning (Exercise 12.2) | Q1 to Q10 | True or False with justification | Properties of combined solids, curved versus total surface area, and how area and volume change when dimensions scale |
| (D) Short Answer (Exercise 12.3) | Q1 to Q12 | Short Answer | Area and volume of combined solids in two or three steps, conversion problems, and slant height of a frustum |
| (E) Long Answer (Exercise 12.4) | Q1 to Q9 | Long Answer | Multi-step problems on cones drilled into cylinders, hemispheres on cylinders, frustum-plus-cylinder shapes, and word problems on tanks and tents |
Why the Exemplar Matters
The Exemplar uses the same ideas as the textbook but raises the bar. The textbook gives a single cylinder or a simple cone; the Exemplar adds a second solid and makes you split the shape into two or three parts. Students who practise only the textbook often freeze on a board problem like the total surface area of a rocket: a cone on a cylinder on a hemisphere.
- Cone-on-Cylinder and Hemisphere-on-Cylinder: The board often asks for the total surface area of a cone or hemisphere set on a cylinder. Exercise 12.4 Q1 to Q4 train this by making you spot which flat circular faces are internal and leave them out.
- Conversion of Solids: A sphere melted into cones, or a cylinder reshaped into spheres, is a repeat board topic. Exercise 12.3 Q7 to Q12 drill it across different radius and height combinations.
- Frustum Problems: Exercise 12.4 Q5 to Q9 train frustums, where you find the slant height first, then the curved surface area, often combined with a base or cylinder to form a bucket or tank.
Exemplar vs NCERT Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table below shows three cases where the step-up is clear, so you know what extra practice the Exemplar gives you.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Surface Area of Combined Solids | Cone mounted on a hemisphere; find the total surface area. | Hemisphere surmounted by a cone; find the total surface area and verify no flat face is double-counted. |
| Volume of Combined Solids | Hollow hemisphere mounted by a hollow cylinder; find the inner surface area. | Two stacked cylinders forming an iron pole; find the mass given the density of iron. |
| Frustum of a Cone | Given slant height and the two perimeters, find the curved surface area. | Cylinder attached to a frustum forming an oil funnel; find the area of tin sheet required. |
The Exemplar always adds a layer: a proof, a decomposition step, or a general expression for the unknown. Students who practise only the textbook often lose 3 to 5 marks per combination problem, because the board now wants the decomposition step shown, not just the final answer.
Full worked solutions: Surface Areas and Volumes Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar does not replace the textbook. Interleave them: read a formula, solve the matching textbook exercise, then try the Exemplar problems on the same concept. A three-day plan keeps the load even.
- Day 1 (Formulae and MCQ): Read the textbook on surface area of a combination of solids. Then try MCQs Exercise 12.1 Q1 to Q6 and reasoning items Exercise 12.2 Q1 to Q5.
- Day 2 (Volume and Short Answer): Read the textbook on volume of combinations and conversion of solids. Finish the rest of the MCQ and reasoning items (12.1 Q7 to Q12, 12.2 Q6 to Q10), then do all of Exercise 12.3 Q1 to Q12 on a 40-minute timer. Write the decomposition step before every calculation.
- Day 3 (Long Answer and Frustum): Read the textbook on the frustum of a cone. Do all of Exercise 12.4 Q1 to Q9 on a 55-minute timer. Write the decomposition, the formula, the substituted values, and the result in full at each stage.
Related Links:
- Surface Areas and Volumes Class 10 Maths NCERT Solutions
- Surface Areas and Volumes Class 10 Maths Notes
PDF Download Formats & Languages
This PDF comes in formats suited to different revision styles. The table below shows what each one is best for, so you can pick the one that fits your study setup.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The English PDF and its Hindi-medium edition use the same notation and question numbering as the printed NCERT 2026-27 release. A few points to know:
- NCERT-faithful: every problem matches the printed Exemplar line for line, including the solved samples with full working.
- Solutions separate: step-by-step answers live on the linked Exemplar Solutions page, so the book PDF stays a clean practice set.
- State-board friendly: state-board students get the same cylinder, cone, sphere, and combination content; only the exercise numbers may differ.
More Resources for This Chapter
- Surface Areas and Volumes Class 10 Maths NCERT Solutions
- Surface Areas and Volumes Class 10 Maths Notes
- Surface Areas and Volumes Class 10 Maths Formula Sheet
- Surface Areas and Volumes Class 10 Maths NCERT Book PDF
- Surface Areas and Volumes Class 10 Maths NCERT Exemplar Solutions
- Surface Areas and Volumes Class 10 Maths Handwritten Notes
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 10 Maths Surface Areas and Volumes: available above as a free PDF download, aligned to the 2026-27 NCERT Class 10 Mathematics syllabus.
| Resource | Link |
|---|---|
| NCERT Solutions | Surface Areas and Volumes NCERT Solutions |
| Notes | Surface Areas and Volumes Class 10 Notes |
| Formula Sheet | Surface Areas and Volumes Formula Sheet |
| NCERT Book PDF | Surface Areas and Volumes NCERT Book PDF |
| Exemplar Solutions | Surface Areas and Volumes Exemplar Solutions |
| Handwritten Notes | Surface Areas and Volumes Handwritten Notes |
NCERT Exemplar Class 10 Maths Surface Areas and Volumes Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Surface Areas and Volumes PDF for free?
Ans. You can download the Surface Areas and Volumes Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Surface Areas and Volumes Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers curved and total surface areas and volumes of combinations of solids, conversion of solid from one shape to another, and the frustum of a cone including its curved surface area and volume formulae.
Ques. How many problems are in the Class 10 Maths Surface Areas and Volumes Exemplar PDF?
Ans. The Surface Areas and Volumes Exemplar PDF contains 43 unsolved problems, split as 12 MCQ (Exercise 12.1), 10 reasoning items (Exercise 12.2), 12 short answer (Exercise 12.3) and 9 long answer (Exercise 12.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Surface Areas and Volumes?
Ans. Yes. The Exemplar introduces multi-step decomposition problems requiring students to split a 3D shape into three or more parts, MCQ on properties of combined solids beyond direct formula use, and true-or-false items that test the logical relationships between surface areas and volumes rather than just numerical answers. This layered style matches the HOTS and long-answer combination problems in recent CBSE Class 10 board papers, which the textbook's more direct problems do not fully prepare students for.
Ques. Should I attempt the Surface Areas and Volumes Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read the textbook section on a formula, solve the matching textbook exercise, then attempt the Exemplar problems on the same concept. Trying the Exemplar first usually leaves students stuck on multi-step combination problems because they have not yet built the single-formula application habit from the textbook.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 12?
Ans. The nine long-answer problems in Exercise 12.4 are closest to the CBSE 5-mark combination-of-solids style. They cover a cone placed on a cylinder where students must identify the exposed curved surfaces, hemisphere-plus-cylinder word problems on water tanks and oil containers, frustum-of-a-cone problems requiring slant height computation before the curved surface area formula can be applied, and real-life earthwork problems involving the volume of soil dug out to form a well or a pit.
Ques. What are the key concepts tested in the Surface Areas and Volumes Exemplar?
Ans. The main concepts tested throughout the Exemplar are: (1) Curved and total surface area of a cylinder, cone, and sphere or hemisphere and which flat circular faces are exposed in a combined solid, (2) Volume of a combined solid as the sum of the individual component volumes, (3) Conversion of a solid from one shape to another by equating volumes, (4) The frustum of a cone including its slant height, curved surface area, total surface area, and volume, (5) MCQ and reasoning on properties of combined solids and relationships between dimensions, and (6) HOTS problems where the combined solid requires three or more separate surface area or volume computations before the final answer can be assembled.
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