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CBSE Class 8 Mathematics Chapter 9 Mensuration Worksheet with Answers

Mensuration is a scoring chapter in CBSE Class 8 Mathematics, contributing 12-15 marks in term examinations. This printable worksheet mirrors the latest NCERT pattern, covering area of trapezium and polygons, surface area of cube, cuboid, and cylinder, plus volume of solids. Print it out, set a timer for 90 minutes, and simulate exam conditions at home to build speed and accuracy before your school tests.

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Key takeaways

✓Worksheet difficulty: Medium to Hard; Suggested time: 90 minutes for complete attempt with self-checking
✓Section A contains 8 MCQs testing fundamental concepts of area, perimeter, surface area, and volume
✓Section B has 6 fill-in-the-blanks focusing on formula recall and unit conversions
✓Section D offers 5 short-answer questions (2-3 marks each) mirroring typical CBSE board patterns
✓Section E includes 3 HOTS long-answer questions demanding multi-step reasoning and application
✓Case-study question integrates real-world scenarios like packaging and construction for applied learning
✓Complete answer key with worked solutions ensures independent practice and immediate feedback

Quick Chapter Recap: Mensuration

Chapter 9 Mensuration in NCERT Class 8 Mathematics extends two-dimensional area concepts to three-dimensional surface area and volume. You already know how to find the area of squares, rectangles, triangles, and circles. This chapter introduces the area of trapezium using the formula ½ × (sum of parallel sides) × height, and shows how to break complex polygons into simpler shapes. The second half dives into solids: cube, cuboid, and cylinder. Surface area splits into lateral (curved) surface area and total surface area. For a cuboid of length l, breadth b, and height h, lateral surface area equals 2h(l + b) and total surface area equals 2(lb + bh + hl). For a cylinder of radius r and height h, curved surface area is 2πrh and total surface area is 2πr(r + h). Volume measures the space inside: V = l×b×h for a cuboid, V = a³ for a cube, and V = πr²h for a cylinder. Mastering unit conversions—1 m² = 10,000 cm², 1 m³ = 1,000,000 cm³, 1 litre = 1,000 cm³—is critical for word problems. The 2024 CBSE Class 8 sample paper allocated 5 marks to mensuration, typically one 3-mark surface-area problem and one 2-mark volume application.

Area of trapezium = ½ × (a + b) × h, where a and b are parallel sides
Cuboid: LSA = 2h(l + b); TSA = 2(lb + bh + hl); Volume = l × b × h
Cylinder: CSA = 2πrh; TSA = 2πr(r + h); Volume = πr²h
Cube: TSA = 6a²; Volume = a³
Always convert all measurements to the same unit before calculation

Section A: Multiple Choice Questions (1 mark each)

This section contains 8 multiple-choice questions testing your grasp of definitions, formulas, and direct applications. Each question has four options; select the correct one. These MCQs mirror the objective-type questions now common in CBSE term-1 exams. Focus on eliminating obviously wrong answers first, then compute or recall the formula. Watch out for unit traps—if the question gives dimensions in metres but answer choices are in square centimetres, convert before comparing. Typical topics include identifying the correct formula, computing surface area or volume with given dimensions, determining the number of faces or edges, and recognising which solid matches a net diagram. Time allocation: aim to finish all 8 MCQs in 12-15 minutes, leaving room to revisit tricky items at the end. Mark your answers on a separate sheet to simulate OMR practice if your school uses bubble sheets for unit tests.

Q1. The curved surface area of a cylinder with radius 7 cm and height 10 cm is: (a) 440 cm² (b) 220 cm² (c) 154 cm² (d) 308 cm²
Q2. Volume of a cube with edge 5 cm is: (a) 25 cm³ (b) 125 cm³ (c) 150 cm³ (d) 75 cm³
Q3. Area of a trapezium with parallel sides 6 cm, 10 cm and height 4 cm is: (a) 32 cm² (b) 24 cm² (c) 64 cm² (d) 40 cm²
Q4. A cuboid has dimensions 4 cm × 3 cm × 2 cm. Its total surface area is: (a) 52 cm² (b) 24 cm³ (c) 26 cm² (d) 48 cm²
Q5. The number of edges in a cube is: (a) 6 (b) 8 (c) 12 (d) 4
Q6. If the radius of a cylinder is doubled and height remains same, curved surface area becomes: (a) double (b) four times (c) half (d) unchanged
Q7. 1 m³ equals: (a) 1000 cm³ (b) 10,000 cm³ (c) 100,000 cm³ (d) 1,000,000 cm³
Q8. The total surface area of a cylinder with r = 3.5 cm and h = 8 cm is (use π = 22/7): (a) 253 cm² (b) 176 cm² (c) 231 cm² (d) 308 cm²

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

Complete each statement with the correct term, number, or formula. This section has 6 blanks designed to test formula recall, terminology, and quick mental math. Read each sentence carefully—some blanks require a numeric answer with units, others need a geometric term like lateral, curved, or total. Common pitfalls include forgetting to square the radius in volume formulas or mixing up TSA and CSA abbreviations. Write answers in the exact form requested; if the blank says 'in cm²', do not write just the number. Precision matters: if the question states 'use π = 22/7', do not approximate with 3.14. Practice writing formulas in standard notation so you can fill them in under exam pressure. Budget roughly 8-10 minutes for this section. If a blank stumps you, leave it and return after finishing easier sections—often a later question will jog your memory.

Q9. The formula for the area of a trapezium is A = ½ × ________ × height.
Q10. The lateral surface area of a cuboid is given by 2 × ________ × (length + breadth).
Q11. Volume of a cylinder with radius r and height h is ________.
Q12. A cube has ________ faces, all of which are identical squares.
Q13. 1 litre is equal to ________ cubic centimetres.
Q14. If the edge of a cube is doubled, its volume becomes ________ times the original volume.

Section C: True or False (1 mark each)

Decide whether each statement is True or False. This section has 5 statements that test conceptual understanding and common misconceptions in mensuration. Simply marking T or F is not enough for practice—mentally justify why a statement is false and what the correct version would be. For instance, if a statement says 'the total surface area of a cuboid equals the sum of areas of all four walls,' recognise it is false because TSA includes top and bottom as well, making it six faces, not four. Pay attention to edge cases: statements involving zero dimensions, negative measurements, or swapped formulas. Some statements may involve proportional reasoning, such as 'If the radius of a cylinder is halved, its volume is also halved'—test with actual numbers if unsure. Allocate about 5-7 minutes for this section. Write T or F clearly; ambiguous marks may lose you easy points in board exams.

Q15. The area of a trapezium depends only on the lengths of its parallel sides. (T/F)
Q16. Lateral surface area of a cylinder excludes the areas of the two circular bases. (T/F)
Q17. A cube is a special case of a cuboid where length, breadth, and height are all equal. (T/F)
Q18. The volume of a cuboid is measured in square units. (T/F)
Q19. Doubling the height of a cylinder doubles its curved surface area. (T/F)

Section D: Short Answer Questions (2-3 marks each)

Answer each question in 30-50 words or show clear working steps. This section contains 5 questions worth 2 or 3 marks each, mirroring typical CBSE board short-answer patterns. You must write the formula first, substitute given values with units, perform the calculation step-by-step, and box or underline the final answer with the correct unit. Marks are often split: 1 mark for writing the correct formula, 1 mark for substitution and calculation, and 1 mark for the final answer. Skipping steps loses you marks even if your final answer is correct. Common question types include computing surface area or volume from given dimensions, finding one dimension when area or volume is given, and comparing two solids. Show all conversions explicitly—if dimensions are in metres and the answer must be in litres, write 1 m³ = 1,000 litres. For part marks, even an incorrect final answer can earn you 1-2 marks if your method is sound. Time budget: roughly 20-25 minutes for all five questions.

Q20. Find the area of a trapezium whose parallel sides are 14 cm and 10 cm, and the distance between them is 6 cm. (2 marks)
Q21. A cuboid has length 8 cm, breadth 5 cm, and height 3 cm. Calculate its total surface area. (3 marks)
Q22. The curved surface area of a cylinder is 264 cm² and its height is 12 cm. Find the radius. (Use π = 22/7) (3 marks)
Q23. A cube has a total surface area of 96 cm². Find the length of its edge. (2 marks)
Q24. How many cubic centimetres of water can a cylindrical tank hold if its radius is 35 cm and height is 50 cm? (Use π = 22/7) (3 marks)

Section E: Long Answer and HOTS Questions (5 marks each)

Solve each problem with detailed step-by-step working. This section has 3 higher-order-thinking questions worth 5 marks each, designed to test application, analysis, and multi-step reasoning. Expect word problems involving cost calculations, painting or tiling areas, volume-to-dimension problems, or comparisons between solids. Read the question twice to identify all given data and what is being asked. Draw a labelled diagram if the problem involves a composite solid or real-world object. Break the solution into clear stages: (1) identify shapes or solids involved, (2) write and apply formulas, (3) perform intermediate calculations with units, (4) combine results, (5) state the final answer with context. For a 5-mark question, examiners typically award 1 mark for the correct approach/formula, 2-3 marks for accurate intermediate steps, and 1 mark for the final answer with unit. Even if you make an arithmetic error, showing logical steps ensures partial credit. Allocate 25-30 minutes for this section. Use the margin to jot down quick checks—does the answer make physical sense? Is the unit correct?

Q25. A room is 6 m long, 4 m wide, and 3 m high. Find the cost of painting its four walls and ceiling at ₹25 per m². (5 marks)
Q26. A cylindrical water tank has a radius of 1.4 m and height 2 m. If it is filled completely, how many litres of water does it hold? Also, find the cost of painting its outer curved surface at ₹10 per m². (Use π = 22/7) (5 marks)
Q27. A cuboid-shaped gift box measures 20 cm × 15 cm × 10 cm. Find (i) the total surface area, (ii) the volume, and (iii) the length of the longest stick that can fit inside the box. (5 marks)

Case-Study Question (4 marks)

Read the scenario carefully and answer the sub-questions that follow. Case-study questions, introduced in recent CBSE papers, assess your ability to extract data from a real-world context and apply mensuration concepts. The passage will describe a practical situation—construction, packaging, gardening, or manufacturing—and provide measurements in prose rather than bullet points. Your job is to parse the text, note down given values with units, identify which solid or shape is involved, and solve 3-4 sub-questions worth 1 mark each. Sub-questions may be MCQ, fill-in-the-blank, or brief calculation type. Underline key numbers and terms as you read. Draw a quick sketch if it helps visualise the setup. Each sub-question is independent, so even if you are unsure about part (i), attempt parts (ii) and (iii). Time budget: 10-12 minutes. This format rewards careful reading and the ability to connect formulas to everyday objects, a skill that also helps in Science practicals and project work.

Complete Answer Key with Explanations

Below are the answers to all sections with brief working or reasoning. Use this key only after attempting the worksheet independently. Self-correction builds deeper understanding than passively reading solutions. For MCQs, verify your choice by reworking the calculation. For descriptive answers, compare your steps—did you write the formula first? Did you convert units? Award yourself marks honestly using the CBSE marking scheme: full credit for complete correct answers, partial credit for correct method with minor errors, zero for wild guesses. If you score below 70 percent on your first attempt, identify weak areas—formula recall, calculation speed, or conceptual gaps—and revise those NCERT sections before trying a second worksheet. Many students find that discussing wrong answers with a peer or tutor cements learning faster than solo review. Platforms like CBSETUTOR.ai offer 24×7 AI tutoring where you can upload a photo of any tricky problem and get a step-by-step video solution instantly, all for a flat ₹999/month across Classes 6-12, with a 3-day free trial to test the feature before committing.

Section A Answers: Q1(a) 440, Q2(b) 125, Q3(a) 32, Q4(a) 52, Q5(c) 12, Q6(a) double, Q7(d) 1,000,000, Q8(a) 253
Section B Answers: Q9: sum of parallel sides; Q10: height; Q11: πr²h; Q12: six; Q13: 1,000; Q14: eight
Section C Answers: Q15 False (height also matters), Q16 True, Q17 True, Q18 False (cubic units), Q19 True
Section D Answers: Q20: 72 cm²; Q21: 158 cm²; Q22: r = 3.5 cm; Q23: edge = 4 cm; Q24: 192,500 cm³
Section E Answers: Q25: ₹2,100; Q26: 12,320 litres, ₹176; Q27: (i) 1,300 cm² (ii) 3,000 cm³ (iii) 25 cm
Case Study Answers: (i) 660 cm² (ii) 968 cm² (iii) 2,310 cm³ (iv) 3.08 m²

How to Use This Worksheet Effectively

Print two copies—one for a timed mock test, the other for untimed practice a week later to measure improvement. Before you start, gather a ruler, compass, calculator (non-programmable as per CBSE rules), and rough paper. Set a timer for 90 minutes and simulate exam conditions: no phone, no breaks, no peeking at notes. Attempt questions in order, but if you are stuck on a long-answer problem, move on and return later—time management is as crucial as content mastery. After 90 minutes, stop and mark your answers with the key. Calculate your raw score, then review each mistake. For calculation errors, redo the problem from scratch. For conceptual mistakes, revisit the corresponding NCERT section and watch a quick video explanation if available. Keep a mistake log: write down the question number, the concept tested, and a one-line note on what went wrong. Before your school exam, review this log—it is a personalised cheat-sheet of your weak spots. Finally, share your score with a study partner or parent; a little accountability boosts consistency. Regular worksheet practice, combined with NCERT exercise solving, can lift your mensuration scores from average to excellence within a month.

Attempt the worksheet in one 90-minute sitting without interruptions
Use only a basic calculator; practice mental math for simple products like 2 × π × 7
Show all working steps even for MCQs; it trains you to avoid silly errors
Self-mark immediately after completing; delayed feedback is less effective
Redo incorrect questions after a day to check if the concept has solidified
Track your scores over multiple worksheets to visualise progress

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Stuck on why the curved surface area formula excludes the base? Wondering how to tackle a tricky case-study faster? CBSETUTOR.ai gives your child a 24×7 AI tutor that answers doubts instantly. Snap a photo of any mensuration problem—whether from this worksheet, NCERT exercises, or your school test paper—and receive a step-by-step video solution in seconds. The platform covers every CBSE subject for Classes 6 to 12 at a single flat rate of ₹999 per month, no hidden fees, no per-subject charges. That is less than the cost of two hours with a private tutor, yet available around the clock. Start with a 3-day free trial: upload five tough problems, explore the interactive formula library, and watch your child's confidence soar. Thousands of families across Delhi NCR, Mumbai, Bengaluru, and Tier-2 cities rely on CBSETUTOR.ai to fill gaps that classroom teaching and YouTube videos leave open. Mensuration becomes less about rote memorising formulas and more about understanding why each formula works—and that understanding is what converts a 60 percent scorer into a 90 percent achiever.

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Frequently asked questions

What is the recommended time to complete this Class 8 Mensuration worksheet?+

Allow yourself 90 minutes under exam conditions. This mirrors a typical CBSE term exam duration for a full Mathematics paper. If you are practising untimed, take breaks but track total active time to gauge speed improvement.

Which formula is most commonly tested in CBSE Class 8 Mensuration exams?+

Curved surface area and volume of a cylinder appear almost every year, often in 3-mark word problems involving water tanks or pipes. Ensure you can recall CSA = 2πrh and V = πr²h instantly, and practise unit conversions to litres.

How do I avoid silly mistakes in surface area calculations?+

Write the formula first, label each term with its value and unit, then substitute. Double-check that you have not confused radius with diameter or mixed up TSA and LSA. A quick dimensional analysis—area must yield square units—catches most errors.

Are case-study questions compulsory in CBSE Class 8 term exams?+

Yes, recent CBSE guidelines mandate at least one 4-mark case-based question per paper. Practising such questions sharpens reading comprehension and application skills, and the marks are often easier to secure than abstract long-answer problems.

What is the difference between lateral surface area and total surface area?+

Lateral (or curved) surface area includes only the side walls—excludes top and bottom. Total surface area adds all faces. For a cuboid, LSA = 2h(l + b); TSA = 2(lb + bh + hl). For a cylinder, CSA = 2πrh; TSA = 2πr(r + h).

How many marks does Chapter 9 Mensuration carry in the Class 8 final exam?+

Typically 12-15 marks out of 80 in the annual exam, distributed across one MCQ (1 mark), one short-answer (2-3 marks), one long-answer or case-study (4-5 marks), and sometimes a fill-in-the-blank or assertion-reason question.

Can I use a calculator for CBSE Class 8 Mathematics exams?+

CBSE allows basic non-programmable calculators for Classes 9-12 board exams, but many schools prohibit them in Class 8 unit tests to build mental-math skills. Check your school's policy and practise both with and without a calculator.

What should I do if I forget the formula for area of a trapezium during the exam?+

Recall that a trapezium can be split into a rectangle and two triangles, or averaged as (average of parallel sides) × height. Deriving Area = ½(a + b)h from basics takes 30 seconds and shows the examiner you understand the concept, often earning partial credit.

How can CBSETUTOR.ai help me prepare for Mensuration?+

Upload photos of worksheet problems you find difficult and receive instant step-by-step solutions. The AI tutor explains why each formula applies, shows unit conversions, and highlights common pitfalls. At ₹999/month for all subjects and classes, it is an affordable alternative to expensive coaching.

Is practising previous years' CBSE question papers enough for Mensuration?+

Previous papers show the exam pattern, but worksheets like this one offer fresh problems and targeted practice. Combine both: solve past papers under timed conditions for exam simulation, then use worksheets to drill weak areas identified in those tests.

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