Math of Space: Surface Area and Volume — 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, "Math of Space: Surface Area and Volume". 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 top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "Math of Space: Surface Area and Volume", 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 Math of Space: Surface Area and Volume, 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.
Math of Space: Surface Area and Volume — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
A cuboid has length 8 cm, width 5 cm and height 3 cm. What is its total surface area?
A.158 cm²✓ CorrectB.79 cm²C.120 cm²D.128 cm²Answer: A. 158 cm²
Explanation: TSA = 2(lw + wh + lh) = 2(40 + 15 + 24) = 2 × 79 = 158 cm². 79 cm² forgets the factor 2 (each face has a matching opposite face), and 120 cm² is the volume in the wrong unit.
- Q2Easy
A cylinder has radius 7 cm and height 10 cm. Find its curved surface area. Use π = 22/7.
A.440 cm²✓ CorrectB.1540 cm²C.748 cm²D.220 cm²Answer: A. 440 cm²
Explanation: CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm². 748 cm² adds the two circular ends (that is the TSA), and 1540 is the volume πr²h.
- Q3Easy
A cone has base radius 5 cm and height 12 cm. What is its slant height?
A.17 cmB.7 cmC.13 cm✓ CorrectD.about 10.9 cmAnswer: C. 13 cm
Explanation: By the Baudhāyana–Pythagoras theorem, l² = h² + r² = 144 + 25 = 169, so l = 13 cm. 17 cm just adds 12 and 5, and about 10.9 cm subtracts the squares instead of adding them.
- Q4Easy
A pyramid has a square base of side 6 cm and height 10 cm. What is its volume?
A.360 cm³B.20 cm³C.240 cm³D.120 cm³✓ CorrectAnswer: D. 120 cm³
Explanation: Base area = 36 cm², so V = (1/3) × 36 × 10 = 120 cm³. 360 cm³ forgets the factor 1/3, and 20 cm³ uses the side 6 instead of the base area 36.
- Q5Easy
Find the surface area of a sphere of radius 7 cm. Use π = 22/7.
A.154 cm²B.308 cm²C.616 cm²✓ CorrectD.about 1437.3 cm²Answer: C. 616 cm²
Explanation: Surface area = 4πr² = 4 × 22/7 × 49 = 616 cm². 154 cm² is πr², one circle only, and 308 cm² is 2πr², the curved surface of a hemisphere.
- Q6Easy
What is a guesstimate question, as described in the chapter?
A.A problem where you must find the exact answer to many decimal placesB.A problem where you make a sensible estimate using assumptions and approximations because exact data are not available✓ CorrectC.A problem where any random guess is as good as any otherD.A problem that can be solved only by measuring the object directlyAnswer: B. A problem where you make a sensible estimate using assumptions and approximations because exact data are not available
Explanation: A guesstimate uses assumptions, approximations, logic and everyday knowledge to model a situation when exact data are missing. Different people may get different answers, but the reasoning matters, so it is not a random guess.
- Q7Medium
How many small cubes of side 25 cm can be packed tightly into a cubical box of side 1.5 m?
A.36B.216✓ CorrectC.18D.1296Answer: B. 216
Explanation: Change 1.5 m to 150 cm. Along each edge, 150 ÷ 25 = 6 cubes fit, so 6 × 6 × 6 = 216 cubes. 36 fills just one layer, and 18 adds instead of multiplying.
- Q8Medium
The radius of cylinder B is 3 times the radius of cylinder A, and the height of B is one third the height of A. Find the ratio of the volume of A to the volume of B.
A.1 : 1B.3 : 1C.1 : 9D.1 : 3✓ CorrectAnswer: D. 1 : 3
Explanation: V is proportional to r²h. For B, r²h = 9 × (1/3) = 3 times that of A, so the volumes of A and B are in the ratio 1 : 3. The ratio 1 : 1 is true for the curved surface areas (rh stays the same), not the volumes.
- Q9Medium
A cone has slant height 25 cm and base diameter 14 cm. Find its total surface area. Use π = 22/7.
A.550 cm²B.704 cm²✓ CorrectC.1716 cm²D.858 cm²Answer: B. 704 cm²
Explanation: r = 7 cm, so TSA = πr(l + r) = 22/7 × 7 × 32 = 704 cm². 550 cm² is the curved part only, and 1716 cm² uses the diameter 14 as the radius.
- Q10Medium
A square pyramid has base side 10 m. Each triangular face has height 13 m (measured along the face). Find its total surface area.
A.360 m²✓ CorrectB.260 m²C.620 m²D.433 m²Answer: A. 360 m²
Explanation: Add all the faces: base 10 × 10 = 100 m² plus four triangles of (1/2) × 10 × 13 = 65 m² each, so 100 + 260 = 360 m². 260 m² leaves out the base, and 620 m² forgets the 1/2 in each triangle.
- Q11Medium
The radius of Mars is about half the radius of the Earth. Taking both as spheres, what is the ratio of the volume of Mars to the volume of the Earth?
A.1 : 2B.1 : 8✓ CorrectC.1 : 4D.1 : 16Answer: B. 1 : 8
Explanation: Volume grows as r³, so (1/2)³ = 1/8 and the ratio is 1 : 8. 1 : 4 is the ratio of their surface areas, which grow as r².
- Q12Hard
A cube of side 7 cm is painted on all faces and then cut into 1 cm cubes. How many small cubes have exactly one face painted?
A.125B.150✓ CorrectC.60D.294Answer: B. 150
Explanation: On each face, the small cubes with only that face painted form a 5 × 5 block (edges and corners removed), so 6 × 25 = 150. 125 = 5³ counts the inside cubes with no paint, and 60 = 12 × 5 counts those with exactly two faces painted.
- Q13Hard
The radius of a cylinder is increased by 10% and its height is decreased by x%. The volume stays the same. What is x (to one decimal place)?
A.21.0B.17.4✓ CorrectC.10.0D.20.0Answer: B. 17.4
Explanation: (1.1)² × (1 − x/100) = 1 gives 1 − x/100 = 1/1.21 ≈ 0.826, so x ≈ 17.4. 21.0 is the percentage rise in r², not the fall in height that cancels it, and 10.0 forgets that the radius is squared.
- Q14Hard
A conical cup (point down) is filled with water up to two-thirds of its depth. What fraction of the cup's volume is filled?
A.8/27✓ CorrectB.2/3C.4/9D.1/3Answer: A. 8/27
Explanation: The water forms a smaller cone with both radius and height scaled by 2/3, so its volume is (2/3)³ = 8/27 of the cup. 4/9 scales only two of the three lengths, and 2/3 scales just one.
Key concepts: Math of Space: Surface Area and Volume (Class 9 Mathematics)
Every solid has a surface (measured in square units) and takes up space (measured in cubic units). This chapter finds surface areas and volumes of cuboids, cubes, cylinders, cones, pyramids, spheres and hemispheres, shows why the formulas work, and uses them to make sensible guesstimates about real things.
- Cuboid and cube
- A cuboid is a 3D rectangle with six rectangular faces and edges l, w, h. A cube is the special cuboid with all edges equal to a side a.
- Volume as unit cubes
- Volume is the number of unit cubes that fit inside a solid, in cm³ or m³. Stacking thin l × w sheets like a pack of cards shows V = area of base × height = lwh.
- Same volume, different surface
- Solids with equal volume can have different surface areas. For a fixed volume a cube needs the least covering, and cutting a solid into small pieces greatly increases the total surface.
- Right circular cylinder
- 'Circular' means the cross-section parallel to the base is a circle; 'right' means the axis is perpendicular to the base. A slice parallel to the axis gives a rectangle.
- Cylinder surface and volume
- Cut open, the curved surface is a rectangle 2πr by h, so CSA = 2πrh. Add one circle for a tumbler (open at one end) or two circles for a closed tin.
- Right circular cone
- Formed by turning a right triangle about one of its legs. The slant height follows from the Baudhāyana–Pythagoras theorem, l² = h² + r².
- Cone surface from the sector
- Unrolled, the curved surface is a sector of radius l whose arc is the base circumference 2πr. So θ/360 = r/l and CSA = πrl.
- Cone volume is one third
- A cone holds one third of the cylinder with the same base and height. Three cone-fulls of salt fill the cylinder, and clay from one cylinder makes exactly three such cones.
- Pyramidal shapes
- Any closed base (triangle, square or other) with every point joined to one apex in a different plane. V = (1/3) × base area × height; a cone is a pyramid with a circular base.
- Pyramid surface area
- There is no special formula: add the areas of the base and all the triangular faces. The face height is not the pyramid's height, which runs from the apex straight down.
- Sphere and Archimedes
- A sphere is all points in space at distance r from a centre. Archimedes showed its surface equals the curved surface of the tight cylinder of height 2r, giving 4πr².
- Sphere volume from thin cones
- Split the surface into tiny pieces joined to the centre to get thin cones of height r. Adding them gives V = (1/3) × 4πr² × r = (4/3)πr³, which is 2/3 of the enclosing cylinder.
- Hemisphere
- Half a sphere cut through its centre: a curved surface 2πr² plus a flat circular base πr², so TSA = 3πr², and its volume is (2/3)πr³.
- Guesstimates and modelling
- When exact data are missing, model the object with simple solids, make sensible assumptions and approximate. Dividing volumes for spheres gives only an upper bound, because spheres leave gaps.
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Start this chapter free →Math of Space: Surface Area and Volume — FAQs
What are the key concepts in Class 9 Mathematics Math of Space: Surface Area and Volume?+
Every solid has a surface (measured in square units) and takes up space (measured in cubic units). This chapter finds surface areas and volumes of cuboids, cubes, cylinders, cones, pyramids, spheres and hemispheres, shows why the formulas work, and uses them to make sensible guesstimates about real things. Key ideas include Cuboid and cube, Volume as unit cubes, Same volume, different surface, Right circular cylinder, Cylinder surface and volume, Right circular cone.
What does Class 9 Mathematics Chapter 14 (Math of Space: Surface Area and Volume) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Math of Space: Surface Area and Volume": 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 "Math of Space: Surface Area and Volume" questions free to practise?+
Yes. Sign in with Google to practise "Math of Space: Surface Area and Volume" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Math of Space: Surface Area and Volume" 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 "Math of Space: Surface Area and Volume" 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 "Math of Space: Surface Area and Volume" 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 Math of Space: Surface Area and Volume (Class 9 Mathematics)?+
The questions that matter most test Cuboid and cube, Volume as unit cubes, Same volume, different surface, Right circular cylinder, Cylinder surface and volume, Right circular cone. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.
Is there an online quiz for Math of Space: Surface Area and Volume?+
Yes — Class 9 Mathematics Math of Space: Surface Area and Volume 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.