Surface Areas and Volumes — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 12
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 12, "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 10 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 10 Mathematics)
Real objects are combinations of cubes, cylinders, cones, spheres and frustums. This chapter computes their surface areas and volumes, joins them into composite solids, and handles the conversion of one solid into another by melting and recasting, where volume is conserved.
- Curved (lateral) surface area
- The area of the curved or side faces only, excluding the flat top and bottom.
- Total surface area
- The curved surface area plus the areas of all flat faces — which faces count depends on whether the solid is open or closed.
- Volume
- The space a solid occupies, measured in cubic units. Capacity is the same quantity expressed in litres.
- Cuboid and cube
- A cuboid has volume l·b·h; a cube is the special case with all edges equal, giving a³.
Surface Areas and Volumes — important questions & MCQs with answers (Class 10 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
Surface area of a sphere of radius r:
A.2πr²B.πr²C.4πr²✓ CorrectD.(4/3)πr³Answer: C. 4πr²
Explanation: Surface area of a sphere = 4πr²; πr² alone is just a circle's area and (4/3)πr³ is the sphere's volume, so keep the exponent and coefficient straight.
- Q2Easy
Total surface area of a cuboid (l, b, h):
A.2(lb + bh + hl)✓ CorrectB.lbhC.l + b + hD.2(l + b + h)Answer: A. 2(lb + bh + hl)
Explanation: The total surface area of a cuboid is 2(lb + bh + hl) — the sum of the areas of its three pairs of faces; lbh is the volume.
- Q3Easy
Volume of a cube with side a is:
A.6a²B.a³✓ CorrectC.a²D.4aAnswer: B. a³
Explanation: Volume of a cube = a³ (side cubed); a² gives only one face's area, and 6a² is the total surface area, not the volume.
- Q4Easy
Volume of a cylinder of radius r and height h is:
A.πr²h✓ CorrectB.2πrhC.πrhD.πr²Answer: A. πr²h
Explanation: Volume of a cylinder = πr²h, the circular base area πr² times height h; 2πrh is only the curved surface area, not the volume.
- Q5Easy
Volume of a cone of radius r and height h is:
A.(1/3)πr²hB.πr²hC.πr²(h/3)D.both a and c✓ CorrectAnswer: D. both a and c
Explanation: Volume of a cone = (1/3)πr²h, the same value as πr²h/3 written differently — both are correct since the ÷3 can sit anywhere in the product.
- Q6Easy
Volume of a sphere of radius r is:
A.πr³B.4πr²C.(2/3)πr³D.(4/3)πr³✓ CorrectAnswer: D. (4/3)πr³
Explanation: Volume of a sphere = (4/3)πr³; dropping the 4/3 factor or confusing it with the surface area formula 4πr² (no r³ term) is the usual slip.
- Q7Medium
Volume of cone radius 3, height 4:
A.12π✓ CorrectB.36πC.24πD.48πAnswer: A. 12π
Explanation: Volume of a cone = (1/3)πr²h = (1/3)π(3²)(4) = 12π. Skipping the ⅓ factor gives 36π, the volume of the matching cylinder instead.
- Q8Medium
A cuboid has dimensions 10 cm × 8 cm × 5 cm. Its total surface area is:
A.340 cm²✓ CorrectB.400 cm²C.180 cm²D.240 cm²Answer: A. 340 cm²
Explanation: TSA of a cuboid = 2(lb + bh + lh) = 2(10×8 + 8×5 + 10×5) = 2(170) = 340 cm². Missing one pair of faces undercounts the total.
- Q9Medium
If total surface area of a cube is 216 cm², its side is:
A.12 cmB.36 cmC.6√6 cmD.6 cm✓ CorrectAnswer: D. 6 cm
Explanation: TSA of a cube = 6a² = 216, so a² = 36 and a = 6 cm. Forgetting to divide by 6 before the square root gives a wrong larger side.
- Q10Medium
A cylinder has radius 14 cm and height 5 cm. Curved surface area (π = 22/7):
A.880 cm²B.308 cm²C.440 cm²✓ CorrectD.220 cm²Answer: C. 440 cm²
Explanation: CSA of a cylinder = 2πrh = 2×(22/7)×14×5 = 440 cm². Using πr²h here computes the volume, not the curved surface area.
- Q11Medium
Slant height of a cone with radius 7 cm and height 24 cm is:
A.31 cmB.25 cm✓ CorrectC.17 cmD.√625 cmAnswer: B. 25 cm
Explanation: Slant height l = √(r² + h²) = √(49 + 576) = √625 = 25 cm, from the right triangle formed by radius, height and slant edge.
- Q12Hard
Two cubes each of volume 64 cm³ are joined end to end. The surface area of the resulting cuboid is:
A.192 cm²B.160 cm²✓ CorrectC.128 cm²D.256 cm²Answer: B. 160 cm²
Explanation: Each cube has edge 4 cm, so the cuboid is 8 × 4 × 4 and its surface area is 2(32 + 16 + 32) = 160 cm².
- Q13Hard
Two cubes of edge 6 cm are joined end to end. Surface area of the resulting cuboid:
A.360 cm²✓ CorrectB.432 cm²C.216 cm²D.288 cm²Answer: A. 360 cm²
Explanation: Joining gives a cuboid 12×6×6, so TSA = 2(lb+bh+lh) = 2(72+36+72) = 360 cm². Doubling one cube's area (432) ignores the hidden joined faces.
- Q14Hard
A hollow cylindrical pipe has outer radius 5 cm and inner radius 4 cm, length 14 cm. Volume of metal in pipe (π = 22/7):
A.440 cm³B.308 cm³C.154 cm³D.396 cm³✓ CorrectAnswer: D. 396 cm³
Explanation: Volume of metal = π(R² − r²)h = (22/7)(25 − 16)(14) = (22/7)(9)(14) = 396 cm³. Squaring (R − r) instead of using R² − r² is the common error.
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Start this chapter free →Surface Areas and Volumes — FAQs
What are the key concepts in Class 10 Mathematics Surface Areas and Volumes?+
Real objects are combinations of cubes, cylinders, cones, spheres and frustums. This chapter computes their surface areas and volumes, joins them into composite solids, and handles the conversion of one solid into another by melting and recasting, where volume is conserved. Key ideas include Curved (lateral) surface area, Total surface area, Volume, Cuboid and cube.
What does Class 10 Mathematics Chapter 12 (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 10 Mathematics)?+
The questions that matter most test Curved (lateral) surface area, Total surface area, Volume, Cuboid and 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 10 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.