Surface Areas and Volumes — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 14
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 14, "Surface Areas and Volumes". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Surface Areas and Volumes", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Surface Areas and Volumes, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Surface Areas and Volumes (Class 9 Mathematics)
Solids are measured by two different quantities: surface area, the covering needed, and volume, the space filled. This chapter gives both for the cuboid, cube, cylinder, cone and sphere, and applies them to real problems of painting, filling and capacity.
- Surface area versus volume
- Surface area is the covering of a solid in square units; volume is the space it occupies in cubic units. Which one a question wants is decided by the context.
- Curved and total surface area
- Curved surface area covers only the side faces; total surface area adds the flat top and base, and whether to include them depends on whether the solid is open.
- Cuboid
- A box-shaped solid with six rectangular faces, measured by its length, breadth and height.
- Cube
- A cuboid with all edges equal, so every formula reduces to a function of the single edge a.
Surface Areas and Volumes — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Total surface area of a cuboid with length l, breadth b, height h is:
A.2(lb+bh+hl)✓ CorrectB.lb+bh+hlC.lbhD.2lbhAnswer: A. 2(lb+bh+hl)
Explanation: Total surface area of a cuboid adds all 3 pairs of opposite faces: TSA = 2(lb+bh+hl). Don't just add lb+bh+hl once — each face pair is counted twice, since a cuboid has 6 faces, not 3.
- Q2Easy
Lateral (curved) surface area of a cylinder with radius r and height h is:
A.πr²hB.2πrh✓ CorrectC.2πr(r+h)D.πrhAnswer: B. 2πrh
Explanation: The curved surface unrolls into a rectangle of width = circumference (2πr) and height h, so LSA = 2πrh. A common slip is using πr²h (that's volume) instead of the curved-surface formula.
- Q3Easy
Slant height l of a cone with base radius r and height h is:
A.√(r+h)B.√(r²−h²)C.r+hD.√(r²+h²)✓ CorrectAnswer: D. √(r²+h²)
Explanation: The radius, height and slant height form a right triangle inside the cone, so by Pythagoras l = √(r²+h²). Adding r and h directly instead of using Pythagoras gives a wrong slant height.
- Q4Easy
Surface area of a sphere with radius r is:
A.πr²B.2πr²C.4πr²✓ CorrectD.4/3 πr³Answer: C. 4πr²
Explanation: Surface area of a sphere is 4πr² — 4 times the area of a great circle (πr²). Mixing this up with volume, (4/3)πr³, is the usual error since both start with the same base value πr³/πr².
- Q5Easy
Total surface area of a cube with edge a is:
A.4a²B.a³C.6a²✓ CorrectD.8a²Answer: C. 6a²
Explanation: A cube has 6 identical square faces of area a² each, so total surface area = 6a². Don't confuse this with volume (a³) — surface area counts flat faces, volume counts the space inside.
- Q6Easy
Total surface area of a closed cylinder is:
A.2πrhB.πr²hC.2πr(r+h)✓ CorrectD.2πr²+hAnswer: C. 2πr(r+h)
Explanation: Total surface area of a closed cylinder = curved surface (2πrh) + two circular ends (2πr²) = 2πr(r+h). Forgetting the two end circles gives only the curved surface area, not the total.
- Q7Medium
Find TSA of a cuboid with l=12cm, b=10cm, h=8cm.
A.720 cm²B.592 cm²✓ CorrectC.480 cm²D.196 cm²Answer: B. 592 cm²
Explanation: TSA = 2(lb+bh+hl) = 2(12×10+10×8+8×12) = 2(120+80+96) = 2×296 = 592 cm². Skipping the final ×2 (forgetting each face pair is counted twice) gives 296, a common half-answer mistake.
- Q8Medium
CSA of cylinder with r=7cm, h=10cm (use π=22/7):
A.880 cm²B.154 cm²C.308 cm²D.440 cm²✓ CorrectAnswer: D. 440 cm²
Explanation: CSA = 2πrh = 2×(22/7)×7×10 = 440 cm². Using r² instead of r — i.e. computing πr²h, the volume formula — is the usual mix-up here.
- Q9Medium
Find slant height of cone with r=6cm, h=8cm.
A.7 cmB.14 cmC.10 cm✓ CorrectD.√28 cmAnswer: C. 10 cm
Explanation: Slant height l = √(r²+h²) = √(36+64) = √100 = 10 cm — the classic 6-8-10 Pythagorean triple. Adding r+h directly (giving 14) skips the Pythagoras step entirely.
- Q10Medium
Find surface area of sphere with r=14cm (π=22/7).
A.2464 cm²✓ CorrectB.1232 cm²C.4928 cm²D.616 cm²Answer: A. 2464 cm²
Explanation: SA = 4πr² = 4×(22/7)×14² = 4×(22/7)×196 = 4×616 = 2464 cm². Forgetting the factor of 4 gives 616 cm², a frequent shortfall in this formula.
- Q11Medium
A room is 5m × 4m × 3m. How many litres of air does it contain? (1m³=1000L)
A.6000 LB.60000 L✓ CorrectC.600 LD.120 LAnswer: B. 60000 L
Explanation: Volume = 5×4×3 = 60 m³, and since 1 m³ = 1000 L, that's 60×1000 = 60000 litres. Forgetting the m³-to-litre conversion and stopping at 60 (or misplacing a zero) is the usual slip.
- Q12Hard
The diagonal of a cuboid 3×4×12 is:
A.13B.19C.√169D.Both a and c✓ CorrectAnswer: D. Both a and c
Explanation: Diagonal = √(l²+b²+h²) = √(9+16+144) = √169 = 13 cm; the plain number 13 and the radical √169 are just two ways of writing the same value, so both together are correct. Treating them as different answers misses that √169 simplifies exactly to 13.
- Q13Hard
A cylindrical tank holds 1540 litres. Base circumference is 440 cm. Find depth (π = 22/7).
A.50 cmB.70 cmC.100 cm✓ CorrectD.140 cmAnswer: C. 100 cm
Explanation: Circumference 2πr = 440 gives r = 70 cm; V = πr²h with V = 1540 L = 1,540,000 cm³ gives 15400h = 1,540,000, so h = 100 cm. Skipping the litre-to-cm³ conversion (1 L = 1000 cm³) is the usual place this goes wrong.
- Q14Hard
A copper sphere r=3cm is melted into a wire r=0.3cm. Find length of wire.
A.1200 cmB.400 cm✓ CorrectC.1800 cmD.600 cmAnswer: B. 400 cm
Explanation: Melting preserves volume: (4/3)π(3)³ = π(0.3)²L gives 36π = 0.09πL, so L = 400 cm. Forgetting that the wire's cross-section uses its own small radius (0.3 cm, not 3 cm) is the common mix-up.
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Start this chapter free →Surface Areas and Volumes — FAQs
What are the key concepts in Class 9 Mathematics Surface Areas and Volumes?+
Solids are measured by two different quantities: surface area, the covering needed, and volume, the space filled. This chapter gives both for the cuboid, cube, cylinder, cone and sphere, and applies them to real problems of painting, filling and capacity. Key ideas include Surface area versus volume, Curved and total surface area, Cuboid, Cube.
What does Class 9 Mathematics Chapter 14 (Surface Areas and Volumes) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Surface Areas and Volumes": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Surface Areas and Volumes" questions free to practise?+
Yes. Sign in with Google to practise "Surface Areas and Volumes" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Surface Areas and Volumes" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Surface Areas and Volumes" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Surface Areas and Volumes" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Surface Areas and Volumes (Class 9 Mathematics)?+
The questions that matter most test Surface area versus volume, Curved and total surface area, Cuboid, Cube. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Surface Areas and Volumes?+
Yes — Class 9 Mathematics Surface Areas and Volumes has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.