India's #1 AI Tutorworksheet · Mathematics · Chapter 12

CBSE Class 10 Mathematics Chapter 12 Surface Areas and Volumes Worksheet with Answers

Surface Areas and Volumes is a high-scoring chapter in CBSE Class 10 Mathematics, typically carrying 8-10 marks in the board exam. This worksheet has been designed to give students focused practice on combinations of solids, conversion between solids, and the frustum of a cone. All questions are rooted in NCERT terminology and the latest examination pattern, ensuring students build both accuracy and speed.

Your child's private AI tutor — trained on NCERT.

3-day free trial · ₹1 to start · Cancel anytime.

Start 3-day free trial →

Key takeaways

✓Worksheet contains 35+ questions designed strictly per the latest CBSE Class 10 Mathematics board exam blueprint for Chapter 12.
✓Covers all NCERT topics: combinations of solids, conversion of one solid to another, and frustum of a cone with practical applications.
✓Section-wise difficulty progression from basic MCQs to HOTS long-answer questions ensures thorough conceptual understanding.
✓Case-study question included to align with the new CBSE competency-based assessment pattern introduced in 2023.
✓Complete answer key with brief working provided for every question, enabling independent practice and immediate feedback.
✓Recommended time limit of 90 minutes helps students build speed and exam temperament for the actual board paper.
✓Printable format suitable for home practice, classroom tests, or revision sessions before half-yearly and annual exams.

Chapter 12 Quick Recap: Surface Areas and Volumes

Before attempting the worksheet, revisit the three core topics in this chapter. Combinations of solids involve finding surface area and volume of objects formed by joining two or more basic shapes like cones, cylinders, hemispheres, and cuboids. For instance, a toy shaped like a cone mounted on a cylinder. Conversion between solids asks: if a sphere is melted and recast into a cylinder, what are the new dimensions? The principle is that volume remains constant during recasting. The frustum of a cone is the solid left when a smaller cone is sliced off from the top of a larger cone parallel to the base. Frustum formulae — surface area = π(r₁ + r₂)l + πr₁² + πr₂² and volume = (1/3)πh(r₁² + r₂² + r₁r₂) — appear frequently in real-life contexts such as buckets, lampshades, and funnels. Mastery of these three topics, combined with careful diagram sketching, ensures near-perfect scoring in this chapter.

Combinations of solids: Add or subtract surface areas carefully; overlapping surfaces are not counted.
Conversion of solids: Equate volumes of the original and new shape, then solve for unknown dimensions.
Frustum formulae must be memorised; r₁ is the larger radius, r₂ the smaller, h the height, l the slant height.
Always write units (cm, m, cm², m³) and use π = 22/7 or 3.14 as instructed in the question.

Worksheet Instructions and Time Allocation

This worksheet is structured to mirror a 40-mark section of the CBSE Class 10 Mathematics board paper. Difficulty level is moderate to challenging, suitable for students who have completed the NCERT exercises at least once. Suggested time is 90 minutes under exam conditions — no calculator, no textbook reference. Attempt all sections sequentially: Section A (MCQs) should take roughly 12 minutes, Section B (fill-in-the-blanks) 10 minutes, Section C (match/true-false) 8 minutes, Section D (short answers) 30 minutes, Section E (long answers and HOTS) 25 minutes, and the case-study question 5 minutes. Use the final few minutes to review calculations and units. After completion, check your answers against the detailed answer key provided at the end. Mark yourself honestly and identify weak areas — whether it is formula recall, diagram interpretation, or arithmetic errors — then revisit those NCERT examples.

Total marks: 40 (indicative). Total questions: 35+. Suggested time: 90 minutes.
Difficulty level: Moderate to challenging, designed for students aiming for 35+ / 40.
Attempt in one sitting without breaks to simulate real exam pressure.
Show all working clearly; marks are awarded for method even if the final answer is incorrect.
Use diagrams wherever possible, especially in Section E long-answer questions.

Section A: Multiple Choice Questions (1 mark each)

Choose the single best answer for each question. No negative marking, but careless reading can cost easy marks. Each MCQ tests one concept sharply — formula recall, unit conversion, or a quick calculation. In the 2025 board exam, 20 out of 80 marks come from MCQs, so practice is essential. Remember to convert all measurements to the same unit before applying formulae, and double-check whether the question asks for total surface area, curved surface area, or volume. Read the options carefully; often two choices differ only in the value of π used or the power of 10 in the final answer.

Section B: Fill in the Blanks (1 mark each)

Complete each statement with the correct mathematical term, formula, or numerical answer. Precision matters: write 'frustum' not 'frustrum', 'slant height' not 'slope'. Units must be included where the blank calls for a measurement. These questions test whether you can recall definitions and standard results without prompting. For instance, you should know that the volume of a sphere is (4/3)πr³ and that when a solid is converted, volume is conserved but surface area generally changes. In fill-in-the-blank questions, spelling and exact phrasing count, so write neatly and double-check before moving on.

Section C: Match the Following / True or False (1 mark each)

This section combines two question types. In match-the-following, pair each item in Column A with exactly one item in Column B; write answers as (i)–(c), (ii)–(a), etc. In true/false, write T or F, and if asked, correct the false statement. These questions check whether you can distinguish between similar-looking formulae — for example, curved surface area versus total surface area, or the volume of a cone versus the volume of a frustum. Read each statement word by word; a single misplaced exponent or missing π can flip the truth value. Marks are easy here if you have revised formulas thoroughly.

Section D: Short Answer Questions (2 marks each)

Each short-answer question requires a brief calculation or derivation, typically 3–5 lines of working. Marks are split: 1 mark for correct method (formula, substitution) and 1 mark for correct final answer with unit. Always state the formula first, substitute given values with units, simplify step by step, and box or underline your final answer. Even if your arithmetic goes wrong, clear method fetches you partial credit. Common pitfalls include forgetting to subtract the overlapping area in combinations of solids, using diameter instead of radius, or mixing up r₁ and r₂ in frustum problems. Practice writing concise, methodical solutions; in the board exam, the examiner spends under 30 seconds per 2-mark question, so clarity is rewarded.

Section E: Long Answer and HOTS Questions (3 or 4 marks each)

Long-answer questions demand multi-step reasoning, careful diagram interpretation, and sometimes proof or derivation. Allocate 5–7 minutes per question. Start by drawing a neat labelled diagram if the question involves a combination of solids or a frustum; examiners award marks for correct diagrams. State all relevant formulae, show every substitution, and simplify algebraically before plugging in numerical values. HOTS (Higher Order Thinking Skills) questions test your ability to synthesize concepts — for example, finding the cost of painting a combination solid, or determining dimensions after conversion under additional constraints like 'height is twice the radius'. These questions differentiate the 90+ scorers from the rest. Practice similar problems from NCERT Exemplar and previous years' board papers. If you are stuck, write down everything you know: formula, diagram, given data. Partial marking is generous in long answers.

Always draw and label diagrams for combinations of solids or frustums.
Write formulae explicitly before substituting numbers; this earns method marks even if calculation is wrong.
Check dimensional consistency: volume must have cubic units, area square units.
HOTS questions may involve cost, percentage increase, or optimization — read the question twice.
Show intermediate steps clearly; skipping steps loses marks even if the final answer is correct.

Case-Study Question (4 marks)

Case-study questions were introduced in CBSE Class 10 Mathematics in 2023 to test real-world application and reading comprehension. A short paragraph describes a practical scenario — construction, manufacturing, daily life — followed by 4 sub-questions (1 mark MCQ + 1 mark MCQ + 2 marks short answer). Read the passage carefully, extract given data, identify the solid shapes involved, and apply the correct formulae. These questions are scoring if you stay calm and methodical. Often the first two MCQs are straightforward, and the final sub-question requires a two-step calculation. Underline key numbers (dimensions, costs, quantities) in the passage before attempting the sub-questions. Time management is crucial; spend no more than 5 minutes on the entire case study.

Read the case-study passage twice; underline dimensions, shapes, and any cost or rate given.
Identify the solids involved — cylinder, cone, sphere, frustum, or combinations.
The first two sub-questions are usually 1-mark MCQs testing direct formula application.
The last sub-question is typically a 2-mark calculation or reasoning problem.
Show working for the 2-mark part even if the passage gives some intermediate values.

Complete Answer Key with Explanations

Below is the complete answer key for all sections. Each answer includes the correct option or numerical value, and a brief working or explanation. Use this key to self-assess after completing the worksheet. Award yourself marks honestly: 1 mark for correct method/formula, 1 mark for correct final answer in short-answer questions. For MCQs and fill-in-the-blanks, it is all or nothing. Tally your score out of 40 and identify topics where you lost marks — then revisit those NCERT examples and solved exercises. Remember, Surface Areas and Volumes is a high-scoring chapter; with focused revision and formula practice, you can secure 9 or 10 out of 10 marks in the board exam. If you need step-by-step video explanations for any question on this worksheet, CBSETUTOR.ai offers 24×7 AI tutoring with photo-upload solving at a flat ₹999/month, one price for every class (6–12), with a 3-day free trial — perfect for clearing doubts instantly before exams.

How to Use This Worksheet for Maximum Benefit

Treat this worksheet as a mock test. Print it, sit in a quiet room, and time yourself strictly for 90 minutes. Do not check answers mid-attempt. After finishing, take a 10-minute break, then mark your own paper using the answer key. Calculate your percentage and identify patterns: Are you losing marks in formula recall (Section B), careless arithmetic (MCQs), or conceptual application (HOTS)? For every wrong answer, write the correct solution in a separate notebook and note the mistake type — formula error, sign error, unit conversion, or misreading the question. Repeat this worksheet after one week to check improvement. If your score is below 30/40, revisit NCERT examples for combinations of solids and frustum, and solve all back-exercises. If you are scoring 35+, challenge yourself with NCERT Exemplar problems and previous years' board questions. Consistent practice on structured worksheets like this one is the single most effective strategy to master Surface Areas and Volumes and secure full marks in Chapter 12.

First attempt: timed, closed-book, no calculator. Simulate real exam conditions.
Self-mark honestly using the answer key; calculate percentage and section-wise accuracy.
For each mistake, write the correct solution and identify the error type (concept/arithmetic/careless).
Retry the worksheet after 5–7 days to measure improvement and reinforce learning.
Supplement with NCERT Exemplar and past board papers for additional challenge.
Use CBSETUTOR.ai for instant doubt-solving: upload a photo of any question and get step-by-step AI explanations 24×7.

Common Mistakes Students Make in Chapter 12 and How to Avoid Them

Even strong students drop marks in Surface Areas and Volumes due to recurring errors. First, confusing radius with diameter: always divide diameter by 2 before substituting into formulae. Second, in combinations of solids, adding total surface areas without subtracting the common overlapping base — for example, a cone on a cylinder shares a circular base, so that area is not part of the external surface. Third, in frustum problems, mixing up r₁ (larger radius) and r₂ (smaller radius), or forgetting to use the slant height l in curved surface area. Fourth, unit inconsistency: if height is in metres and radius in centimetres, convert everything to the same unit before calculating. Fifth, in conversion problems, students sometimes equate surface areas instead of volumes; remember, volume is conserved during melting and recasting, not surface area. Sixth, rounding π too early: use 22/7 or 3.14 only in the final step, not in intermediate calculations. Seventh, neglecting to write units in the final answer costs marks even if the number is correct. Make a checklist of these pitfalls and review it before every worksheet or test.

Always halve the diameter to get radius before using any formula.
In combination solids, subtract the area of common/overlapping surfaces from the sum of individual surface areas.
In frustum, r₁ > r₂; double-check which is which before substituting.
Convert all dimensions to the same unit (preferably cm or m) at the start.
Volume is conserved in melting/recasting; surface area is not — never equate surface areas in conversion problems.
Use exact values of π (22/7 or leave as π) until the final answer; only then approximate.
Always state the unit in your final answer: cm, cm², cm³, m, m², m³, or ₹ for cost.
Draw and label diagrams for every long-answer question; it clarifies your own thinking and earns method marks.

Connecting Worksheet Practice to Board Exam Success

The CBSE Class 10 Mathematics board paper in 2025 follows a competency-based blueprint: 20 marks from MCQs, 20 marks from short answers (2–3 marks), 20 marks from long answers (4–5 marks), and typically 4–6 marks from case-study questions. Chapter 12 Surface Areas and Volumes contributes approximately 8–10 marks across these categories. Worksheets like this one train you to handle every question type under time pressure. By practising 3–4 such worksheets before your exams, you internalize formula patterns, reduce silly mistakes, and build the confidence to attempt HOTS questions without panic. The repetitive nature of worksheet practice — read, identify solid, choose formula, substitute, solve — creates muscle memory that frees up mental bandwidth during the actual exam for careful checking and neat presentation. Schools in Delhi, Mumbai, Bengaluru, and other metros often conduct weekly worksheet-based tests in Class 10; if your school does not, self-administer these worksheets at home every weekend. Track your scores in a notebook and aim for consistent improvement. Remember, the board exam rewards clarity, correct formulae, and complete working — all skills honed through disciplined worksheet practice.

CBSE 2025 blueprint: ~10 marks from Chapter 12, spread across MCQs, short answers, long answers, and case study.
Worksheets simulate real exam pressure and train time management and formula recall under stress.
Practise 3–4 full-length worksheets per chapter in the month before board exams.
Track your scores over time to identify improvement trends and persistent weak areas.
Worksheet practice builds 'muscle memory' for standard problem types, freeing cognitive load for HOTS questions.
Schools often use worksheets for periodic tests; if yours does not, self-administer them at home on weekends.
Combine worksheet practice with NCERT exercise solving and previous years' board papers for comprehensive preparation.

Frequently asked questions

How many marks does Chapter 12 Surface Areas and Volumes carry in the CBSE Class 10 board exam?+

Chapter 12 typically contributes 8–10 marks in the CBSE Class 10 Mathematics board exam, spread across MCQs (1–2 questions), short-answer questions (2–3 marks each), one long-answer or HOTS question (4 marks), and occasionally a case-study sub-question. The exact distribution varies yearly, but Surface Areas and Volumes is a high-weightage chapter.

What is the difference between total surface area and curved surface area in combinations of solids?+

Curved surface area (CSA) includes only the curved or lateral surfaces, excluding flat bases or tops. Total surface area (TSA) includes all external surfaces. In a combination like a cone on a cylinder, TSA = CSA(cylinder) + CSA(cone) + area of the base; the common circular top where cone and cylinder meet is not counted because it is internal, not external.

How do I remember the frustum formulae for volume and surface area?+

Use mnemonics and diagrams. For volume, V = (1/3)πh(r₁² + r₂² + r₁r₂), think 'one-third π height times (big square, small square, big times small)'. For curved surface area, CSA = π(r₁ + r₂)l, remember 'π times sum of radii times slant'. Write these on a flashcard and revise daily for a week; they will stick.

Why do we conserve volume and not surface area when melting and recasting solids?+

Volume measures the amount of material (mass, assuming constant density), which does not change during melting and recasting. Surface area measures the external boundary, which depends on shape; a sphere and a cylinder of the same volume have different surface areas. Hence, equate volumes in conversion problems, never surface areas.

How can I avoid silly mistakes in MCQs on Surface Areas and Volumes?+

Read each option carefully before choosing; often two options differ only in a factor of π or a power of 10. Always convert diameter to radius before substituting. Double-check units and ensure you are answering what is asked — volume, CSA, TSA, or cost. Eliminate obviously wrong options first, then calculate for the remaining choices.

What is the best way to practice combinations of solids for the board exam?+

Draw every combination neatly: label all dimensions and identify individual solids (cone, cylinder, hemisphere, etc.). Write the formula for each component, compute separately, then add or subtract as needed (subtracting overlapping areas). Solve all NCERT examples and back-exercises, then attempt worksheet questions. Repetition builds pattern recognition and speed.

How much time should I spend on the case-study question in the exam?+

Allocate no more than 5 minutes for the entire case-study question (4 marks). The first two MCQs are usually direct and take 1 minute each; the final 2-mark sub-question requires a short calculation, about 3 minutes. Underline key data in the passage before attempting, and move on if you are stuck — do not let one case study eat into time for other high-value questions.

Is it necessary to show working for 1-mark MCQs and fill-in-the-blanks?+

Officially, no rough work is required for MCQs and fill-in-the-blanks; you only tick or write the answer. However, doing rough calculations in the margin helps you avoid careless errors and allows you to double-check if time permits. For fill-in-the-blanks, especially formula-based ones, jot the formula in rough to ensure correct recall.

How does CBSETUTOR.ai help with Surface Areas and Volumes worksheets and doubts?+

CBSETUTOR.ai offers 24×7 AI-powered tutoring: upload a photo of any worksheet question and receive step-by-step solutions instantly. The platform covers all CBSE Class 10 Mathematics chapters, including Surface Areas and Volumes, at a flat ₹999/month for all classes (6–12). A 3-day free trial lets you test the service before subscribing — ideal for clearing doubts at night or during weekend worksheet practice.

Can I use this worksheet for school periodic tests and pre-board exams?+

Absolutely. This worksheet is designed to match the CBSE board exam pattern and difficulty level, making it perfect for school unit tests, periodic assessments, and pre-board exams. Print multiple copies to retry after a gap, or share with classmates for group study sessions. Consistent practice on such worksheets significantly boosts scores in Chapter 12.

Related resources

Important Questions: CBSE Class 10 Mathematics Chapter 12 Surface Areas and Volumes Class 10 Mathematics Chapter 12 Surface Areas and Volumes — Formulas & Key Points Important Questions: CBSE Class 10 Mathematics Chapter 11 Areas Related to Circles Class 10 Mathematics Chapter 11 Areas Related to Circles — Formulas & Key Points AI Tutor for Class 10: The Smart Alternative to Tuition AI Tutor for Class 10 Maths: Learn Faster with Instant Help Class 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting Points CBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

Keep learning — related guides

Class 10Mathematics

Class 10 Maths Tuition in Narela Shankari Bhopal for CBSE

Class 10Mathematics

Class 10 Maths Tuition in Janakpuri - Score 100/100

Class 10Mathematics

Best Maths Tuition for Class 10 in Sikandra Agra

Class 10Mathematics

Important Questions: CBSE Class 10 Mathematics Chapter 14 Probability

Class 10Mathematics

CBSE Class 10 Mathematics Chapter 14 Probability Worksheet with Answers

Class 10Mathematics

Class 10 Mathematics Chapter 14 Probability — Formulas & Key Points

Ready to give your Class 10 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 10 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →