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Surface Areas and Volumes — Class 10 MCQs with Answers

Class 10 CBSE Mathematics · Chapter 12

108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated

Jump to the 6 solved questions

Practise the most important Class 10 CBSE Mathematics questions from Chapter 12, "Surface Areas and Volumes". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.

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 helps you stay accurate when time is short, just 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. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.

Surface Areas and Volumes — important questions & MCQs with answers (Class 10 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

  1. Q1 of 6Easy

    Surface area of a sphere of radius r:

    Show answer

    Answer: 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.

  2. Q2 of 6Easy

    Total surface area of a cuboid (l, b, h):

    Show answer

    Answer: 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.

  3. Q3 of 6Medium

    If total surface area of a cube is 216 cm², its side is:

    A cube drawn in oblique view with its edge marked with a question mark, and the caption: Total surface area = 216 cm².

    Show answer

    Answer: 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.

  4. Q4 of 6Medium

    Assertion (A): A cylindrical glass with a raised hemispherical portion at its bottom holds less than πr²h, where r and h are its inner radius and height. Reason (R): The curved surface area of a hemisphere of radius r is 2πr².

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    Answer: Both A and R are true but R is not the correct explanation of A

    Explanation: Both are true. The glass holds less because the volume of the hemisphere, (2/3)πr³, is taken away from πr²h. R gives the surface area of a hemisphere, not its volume, so R does not explain A.

  5. Q5 of 6Hard

    The radii of two right circular cones are in ratio 3 : 4. If their heights are in ratio 5 : 4, ratio of their volumes:

    Two cones drawn side by side. The first has base radius r₁ and height h₁, the second base radius r₂ and height h₂, with r₁ : r₂ = 3 : 4 and h₁ : h₂ = 5 : 4, as stated in the captions.

    Show answer

    Answer: 45 : 64

    Explanation: Volume ratio = (r₁/r₂)² × (h₁/h₂) = (3/4)² × (5/4) = (9/16) × (5/4) = 45/64. Using the radius ratio directly instead of squaring it is a common mistake.

  6. Q6 of 6Hard

    Assertion (A): A bird-bath is a cylinder of height 1.45 m and radius 30 cm with a hemispherical depression at one end. Its total surface area is 3.3 m². (Use π = 22/7.) Reason (R): The volume of a solid formed by joining two basic solids is the sum of their volumes.

    Show answer

    Answer: Both A and R are true but R is not the correct explanation of A

    Explanation: Both are true. A comes from 2πrh + 2πr² = 2 × (22/7) × 30 × (145 + 30) = 33000 cm² = 3.3 m². R is about volume, not surface area, so it does not explain A.

Surface Areas and Volumes notes: key concepts (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.
Cylinder
A solid with two circular ends; its curved surface unrolls into a rectangle of width 2πr and height h.
Cone
A solid tapering from a circular base to a point, described by its radius, vertical height and slant height.
Slant height
The distance from the cone's apex to the edge of its base, linked to r and h by Pythagoras: l² = r² + h².
A right circular cone with base radius r, vertical height h along the dashed axis from the centre of the base to the apex, and slant height l along its side from the edge of the base to the apex. The radius, height and slant height form a right triangle with the right angle at the centre of the base. Below: l² = r² + h².
Sphere and hemisphere
A sphere has surface area 4πr²; a hemisphere adds its flat circular face, giving a total surface area of 3πr².
Combination of solids
Composite objects such as a cone on a hemisphere; add only the EXPOSED surfaces, since joined faces disappear from the total.
A toy made of a cone standing on a hemisphere of the same radius r: the hemisphere is below, curved side down, and the cone rises from its flat face to a point, with height h. The circle where the two solids join is drawn dashed and labelled joined face: it is inside the toy, not on its surface, so the surface area is the curved surface of the cone plus the curved surface of the hemisphere.
Hidden and shared faces
Where two solids meet, the touching circles are no longer on the surface — including them is the standard error in composite problems.
Frustum of a cone
The solid left when a cone is cut by a plane parallel to its base and the top is removed, described by two radii and a height.
A cone cut by a plane parallel to its base. The small cone removed from the top is drawn dashed. What is left is the frustum, shaded: a bottom circle of radius r₁, a smaller top circle of radius r₂, the height h between them along the dashed axis, and the slant height l along its side.
Melting and recasting
When a solid is melted and reshaped its VOLUME is unchanged while its surface area is not, so equate volumes to find the new dimensions.
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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, Cylinder, Cone.

What does Class 10 Mathematics Chapter 12 (Surface Areas and Volumes) cover on XamBaaz?+

It has 108 NCERT-based MCQs on "Surface Areas and Volumes": 31 Easy, 39 Medium and 38 Hard. Together they make 11 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. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. 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 11 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. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step 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, Cylinder, Cone. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.

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.

Are there question answers and extra questions for Surface Areas and Volumes (Class 10 Mathematics)?+

Yes. This page has 6 solved questions on Surface Areas and Volumes, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.

Are there assertion–reason and case study questions for Surface Areas and Volumes (Class 10 Mathematics)?+

Yes. The Surface Areas and Volumes question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.

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