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By rohit.pandey1
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Updated on 4 Nov 2025, 17:42 IST
Here is 50+ MCQ Questions for Class 8 Maths Chapter 11 Mensuration to put you on the fast track to full marks. Mensuration is a scoring, formula-based chapter, and these MCQs with detailed answers will help you test your understanding, fix mistakes, and build speed for your exam.
Important questions cover area of trapezium, area of a polygon, area of circle and semicircle, volume of a cube and cuboid, volume of a cylinder, total surface area and lateral surface area of a cuboid, perimeter and curved surface area problems. Use as an online test or printable worksheet to identify strengths and weaknesses, revise key Mensuration formulas in context, and turn practice into precision.
Keep this section open while solving problems. It lists essential formulas for trapezium, rhombus, cuboid, cube, and cylinder, including area, lateral/curved surface area, total surface area, and volume.
| Shape | Formula for Area | Formula for Lateral/Curved Surface Area (LSA/CSA) | Formula for Total Surface Area (TSA) | Formula for Volume |
| Trapezium | ½ × (sum of parallel sides) × height | — | — | — |
| Rhombus | ½ × (d1 × d2) | — | — | — |
| Cuboid | — | 2h(l + b) | 2(lb + bh + hl) | l × b × h |
| Cube | — | 4a2 | 6a2 | a3 |
| Cylinder | — | 2πrh | 2πr(r + h) | πr2h |
Strengthen conceptual understanding of Mensuration Class 8 by solving these MCQs on the area of 2D shapes. Each question focuses on key topics like area of trapezium, area of rhombus, and area of polygons, which are frequently asked in CBSE Class 8 Maths Chapter 11 – Mensuration. Regular practice of these questions helps improve speed, accuracy, and formula retention for exams.
Q1. The parallel sides of a trapezium are 10 cm and 12 cm, and the distance between them is 5 cm. What is its area?
(a) 55 cm²
(b) 60 cm²
(c) 110 cm²
(d) 22 cm²
Correct Answer: (b) 55 cm²
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Explanation:
Area = ½ × (10 + 12) × 5 = 11 × 5 = 55 cm².
Final Answer: 55 cm².
Q2. The diagonals of a rhombus are 8 cm and 6 cm. Its area is —
(a) 48 cm²
(b) 24 cm²
(c) 14 cm²
(d) 96 cm²
Correct Answer: (b) 24 cm²
Explanation:
Area = ½ × d₁ × d₂ = ½ × 8 × 6 = 24 cm².
Q3. If one diagonal of a rhombus is 16 cm and its area is 96 cm², the other diagonal is —
(a) 12 cm
(b) 6 cm
(c) 8 cm
(d) 24 cm
Correct Answer: (a) 12 cm
Explanation:
Area = ½ × d₁ × d₂ → 96 = ½ × 16 × d₂
⟹ d₂ = (96 × 2) / 16 = 12 cm.
Q4. The sides of a parallelogram are 12 cm and 8 cm, and the included angle is 90°. What is its area?
(a) 96 cm²
(b) 64 cm²
(c) 20 cm²
(d) 80 cm²
Correct Answer: (a) 96 cm²
Explanation:
Area = base × height = 12 × 8 = 96 cm² (since angle = 90°, height = side).
Q5. The perimeter of a square is 40 cm. What is its area?
(a) 100 cm²
(b) 64 cm²
(c) 144 cm²
(d) 256 cm²
Correct Answer: (a) 100 cm²
Explanation:
Side = 40 ÷ 4 = 10 cm → Area = 10² = 100 cm².
Q6. The base and height of a triangle are 15 cm and 8 cm respectively. Find the area.
Correct Answer: 60 cm²
Explanation:
Area = ½ × base × height = ½ × 15 × 8 = 60 cm².
Q7. The diagonals of a kite are 20 cm and 14 cm. Find its area.
Correct Answer: 140 cm²
Explanation:
Area = ½ × d₁ × d₂ = ½ × 20 × 14 = 140 cm².
Q8. The sides of a rectangle are 14 cm and 8 cm. Find its area.
Correct Answer: 112 cm²
Explanation:
Area = length × breadth = 14 × 8 = 112 cm².
Q9. A square field has an area of 169 m². Find its side.
Correct Answer: 13 m
Explanation: Side = √169 = 13 m.
Q10. A regular hexagon has side 10 cm. If divided into 6 equilateral triangles, find its area using the formula ( \frac{3\sqrt{3}}{2}a^2 ).
Correct Answer: 259.8 cm² (approx.)
Q11. Find the area of a parallelogram whose base is 18 cm and height is 10 cm.
Correct Answer: 180 cm²
Q12. The height of a triangle is 8 cm and its area is 40 cm². Find the base.
Correct Answer: 10 cm
Explanation: 40 = ½ × base × 8 ⟹ base = 10 cm.
Q13. The length of one parallel side of a trapezium is 25 cm, the other is 15 cm, and the height is 8 cm. Find its area.
Correct Answer: 160 cm²
Explanation: Area = ½ × (25 + 15) × 8 = ½ × 40 × 8 = 160 cm².
Q14. The diagonals of a rhombus measure 18 cm and 12 cm. Calculate its area.
Correct Answer: 108 cm²
Explanation: Area = ½ × 18 × 12 = 108 cm².
Q15. The area of a parallelogram is 72 cm² and the base is 9 cm. Find its height.
Correct Answer: 8 cm
Explanation: Area = base × height → height = 72 ÷ 9 = 8 cm.
Q16. The total surface area of a cube with side 5 cm is:
a). 100 cm²
b). 125 cm²
c). 150 cm²
d). 150 cm³
Solution: For a cube, TSA = 6a². Given a = 5 cm, TSA = 6 × 25 = 150 cm².
Answer: (c) 150 cm²
Q17. The lateral surface area of a cuboid with dimensions 10 m × 5 m × 3 m is:
a). 90 m²
b). 180 m²
c). 150 m²
d). 300 m²
Solution: LSA = 2h(l + b) = 2 × 3 × (10 + 5) = 6 × 15 = 90 m².
Answer: (a) 90 m²
Q18. The curved surface area of a cylinder with radius 7 cm and height 10 cm is: (Take π = 22/7)
a). 440 cm²
b). 220 cm²
c). 748 cm²
d). 440 cm³
Solution: CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
Answer: (a) 440 cm²
Q19. The cost of painting the four walls of a room (LSA) is Rs. 520. If the room has a length of 8 m, breadth of 5 m, and height of 4 m, what is the cost of painting per sq. m?
a). Rs 10
b). Rs 5.75
c). Rs 4.03
d). Rs 5.00
Solution: LSA = 2h(l + b) = 2 × 4 × (8 + 5) = 8 × 13 = 104 m². Cost/m² = 520 ÷ 104 ≈ Rs 5.00.
Answer: (d) Rs 5.00
Q20. The total surface area of a cuboid with dimensions 6 cm × 4 cm × 2 cm is:
a). 48 cm²
b). 88 cm²
c). 68 cm²
d). 104 cm²
Solution: TSA = 2(lb + bh + hl) = 2[(6×4) + (4×2) + (2×6)] = 2(24 + 8 + 12) = 88 cm².
Answer: (b) 88 cm²
Q21. If the lateral surface area of a cube is 64 cm², then the length of its side is:
a). 4 cm
b). 8 cm
c). 16 cm
d). 2 cm
Solution: LSA = 4a² = 64 ⇒ a² = 16 ⇒ a = 4 cm.
Answer: (a) 4 cm
Q22. The total surface area of a cylinder with radius 3.5 cm and height 8 cm is: (Take π = 22/7)
a). 253 cm²
b). 176 cm²
c). 220 cm²
d). 154 cm²
Solution: TSA = 2πr(r + h) = 2 × (22/7) × 3.5 × 11.5 = 22 × 11.5 = 253 cm².
Answer: (a) 253 cm²
Q23. A closed cylindrical tank has diameter 14 m and height 5 m. The area of the metal sheet required to make it is: (Take π = 22/7)
a). 440 m²
b). 528 m²
c). 308 m²
d). 616 m²
Solution: TSA = 2πr(r + h) with r = 7 m ⇒ TSA = 2 × (22/7) × 7 × (7 + 5) = 44 × 12 = 528 m².
Answer: (b) 528 m²
Q24. The lateral surface area of a cube is 256 cm². Its total surface area is:
a). 384 cm²
b). 512 cm²
c). 256 cm²
d). 192 cm²
Solution: 4a² = 256 ⇒ a² = 64 ⇒ a = 8 cm. TSA = 6a² = 6 × 64 = 384 cm².
Answer: (a) 384 cm²
Q25. An open cylindrical vessel (without top) has radius 7 cm and height 10 cm. The area of metal sheet required to make it is: (Take π = 22/7)
a). 594 cm²
b). 440 cm²
c). 154 cm²
d). 286 cm²
Solution: Area = CSA + area of base = 2πrh + πr² = 440 + 154 = 594 cm².
Answer: (a) 594 cm²
Q26. If the dimensions of a cuboid are doubled, its total surface area becomes:
a). 2 times
b). 4 times
c). 8 times
d). 16 times
Solution: New TSA = 4 × original TSA (since each term in lb + bh + hl scales by 4).
Answer: (b) 4 times
Q27. The ratio of lateral surface area to total surface area of a cube is:
a). 1:2
b). 2:3
c). 3:4
d). 4:6
Solution: LSA:TSA = 4a² : 6a² = 4 : 6 = 2 : 3.
Answer: (b) 2:3
Q28. A cylindrical pillar has radius 21 cm and height 4 m. The cost of painting its curved surface at Rs. 5 per sq. m is: (Take π = 22/7)
a). Rs 26.40
b). Rs 52.80
c). Rs 264
d). Rs 13.20
Solution: Convert r = 0.21 m. CSA = 2πrh = 2 × (22/7) × 0.21 × 4 = 5.28 m². Cost = 5.28 × 5 = Rs 26.40.
Answer: (a) Rs 26.40
Q29. A cuboid has dimensions in the ratio 3:2:1 and its total surface area is 88 cm². The volume of the cuboid is:
a). 24 cm³
b). 48 cm³
c). 72 cm³
d). 96 cm³
Solution: Let dimensions be 3x, 2x, x. TSA = 2(6x² + 2x² + 3x²) = 22x² = 88 ⇒ x² = 4 ⇒ x = 2. Volume = 6×4×2 = 48 cm³.
Answer: (b) 48 cm³
Q30. The curved surface area of a cylinder is 264 cm² and its height is 14 cm. The radius of the cylinder is: (Take π = 22/7)
a). 3 cm
b). 6 cm
c). 7 cm
d). 4 cm
Solution: CSA = 2πrh ⇒ 264 = 2 × (22/7) × r × 14 = 88r ⇒ r = 3 cm.
Answer: (a) 3 cm
Q31. The volume of a cylinder with a base radius of 7 cm and height of 5 cm is: (Take π = 22/7)
A). 770 cm³
B). 154 cm³
C). 385 cm³
D). 770 cm²
Solution: Volume of cylinder = πr²h
Given: r = 7 cm, h = 5 cm, π = 22/7
V = (22/7) × 7² × 5 = 770 cm³
Answer: (A) 770 cm³
Q32. A cuboidal water tank is 6 m long, 5 m wide, and 4.5 m deep. How many litres of water can it hold? (1 m³ = 1000 L)
A). 135 L
B). 1350 L
C). 13500 L
D). 135000 L
Solution: Volume = l × b × h = 6 × 5 × 4.5 = 135 m³
Capacity = 135 × 1000 = 135000 L
Answer: (D) 135000 L
Q33. The volume of a cube is 64 cm³. What is the length of its side?
A). 4 cm
B). 8 cm
C). 16 cm
D). 2 cm
Solution: Volume = a³ → a³ = 64 → a = 4 cm
Answer: (A) 4 cm
Q34. A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out is 14 m³, what is the depth of the pit?
A). 1.2 m
B). 0.8 m
C). 1 m
D). 0.5 m
Solution: Volume = l × b × h → 14 = 5 × 3.5 × h → h = 14 ÷ 17.5 = 0.8 m
Answer: (B) 0.8 m
Q35. A cuboid has dimensions 8 cm × 6 cm × 5 cm. Its volume is:
A). 240 cm³
B). 120 cm³
C). 480 cm³
D). 240 cm²
Solution: Volume = l × b × h = 8 × 6 × 5 = 240 cm³
Answer: (A) 240 cm³
Q36. A cylindrical water tank has a radius of 1.4 m and height of 2 m. The capacity of the tank is: (Take π = 22/7)
A). 12.32 L
B). 1232 L
C). 12320 L
D). 123.2 L
Solution: Volume = πr²h = (22/7) × 1.4² × 2 = 12.32 m³
Capacity = 12.32 × 1000 = 12320 L
Answer: (C) 12320 L
Q37. The side of a cube is doubled. Its volume becomes:
A). 2 times
B). 4 times
C). 6 times
D). 8 times
Solution: Original volume = a³ → New volume = (2a)³ = 8a³
Answer: (D) 8 times
Q38. How many cubes of side 2 cm can be cut from a cuboid of dimensions 10 cm × 8 cm × 6 cm?
A). 60
B). 120
C). 30
D). 240
Solution: Volume of cuboid = 10 × 8 × 6 = 480 cm³; Volume of cube = 2³ = 8 cm³; No. of cubes = 480 ÷ 8 = 60
Answer: (A) 60
Q39. A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in it. The volume of water displaced is: (Take π = 22/7)
A). 77 cm³
B). 154 cm³
C). 231 cm³
D). 308 cm³
Solution: Volume of cone = (1/3)πr²h = (1/3) × (22/7) × 3.5² × 6 = 77 cm³
Answer: (A) 77 cm³
Q40. A rectangular water reservoir contains 42000 litres of water. If the length is 6 m and breadth is 3.5 m, the height of water level is:
A). 2 m
B). 3 m
C). 4 m
D). 5 m
Solution: Volume = 42 m³ (since 42000 ÷ 1000); 42 = 6 × 3.5 × h → h = 42 ÷ 21 = 2 m
Answer: (A) 2 m
Q41. The volume of a cube is 729 cm³. The length of its edge is:
A). 9 cm
B). 27 cm
C). 81 cm
D). 18 cm
Solution: a³ = 729 → a = ∛729 = 9 cm
Answer: (A) 9 cm
Q42. A cylindrical pipe has inner diameter 7 cm and water flows through it at 20 cm/s. How much water will fall in a tank in 5 minutes? (Take π = 22/7)
A). 231 L
B). 46.2 L
C). 4.62 L
D). 4620 L
Solution: r = 3.5 cm, h = 20 × 300 = 6000 cm; Volume = πr²h = (22/7) × 12.25 × 6000 = 231000 cm³ = 231 L
Answer: (A) 231 L
Q43. The ratio of volumes of two cubes is 8:27. The ratio of their edges is:
A). 2:3
B). 4:9
C). 8:27
D). 1:3
Solution: Volume ratio = a³ : b³ = 8 : 27 → a : b = ∛8 : ∛27 = 2 : 3
Answer: (A) 2:3
Q44. A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, the edge of the third cube is:
A). 10 cm
B). 12 cm
C). 14 cm
D). 16 cm
Solution: V₁ = 12³ = 1728; V₂ = 6³ + 8³ = 216 + 512 = 728; V₃ = 1728 − 728 = 1000; a = ∛1000 = 10 cm
Answer: (A) 10 cm
Q45. A hollow cylindrical pipe is 21 cm long. Its outer and inner diameters are 10 cm and 6 cm respectively. The volume of metal used is: (Take π = 22/7)
A). 1056 cm³
B). 528 cm³
C). 2112 cm³
D). 264 cm³
Solution: V = π(R² − r²)h = (22/7) × (25 − 9) × 21 = 22 × 16 × 3 = 1056 cm³
Answer: (A) 1056 cm³
Q46. If the side of a cube is doubled, its volume will become:
Options:
(a) 2 times
(b) 4 times
(c) 8 times
(d) 16 times
Solution:
Original volume of cube = a³
When side is doubled, new side = 2a
New volume = (2a)³ = 8a³
New volume = 8 × Original volume
Answer: (c) 8 times
Q47. If the radius of a cylinder is halved and its height is doubled, its volume will be:
Options:
(a) Halved
(b) Doubled
(c) The same
(d) Four times
Solution:
Original volume = πr²h
New radius = r/2, New height = 2h
New volume = π(r/2)²(2h) = π × (r²/4) × 2h = πr²h/2
New volume = (1/2) × Original volume
Answer: (a) Halved
Q48. How many 3 cm cubes can be cut out from a cuboid of dimensions 18 cm × 12 cm × 9 cm?
Options:
(a) 72
(b) 64
(c) 80
(d) 75
Solution:
Volume of cuboid = 18 × 12 × 9 = 1944 cm³
Volume of one small cube = 3³ = 27 cm³
Number of cubes = 1944 ÷ 27 = 72
Alternative method:
Along length: 18 ÷ 3 = 6 cubes
Along breadth: 12 ÷ 3 = 4 cubes
Along height: 9 ÷ 3 = 3 cubes
Total cubes = 6 × 4 × 3 = 72
Answer: (a) 72
Q49. A rectangular sheet of paper 44 cm × 18 cm is rolled along its length to form a cylinder. The volume of the cylinder is: (Take π = 22/7)
Options:
(a) 2772 cm³
(b) 1386 cm³
(c) 5544 cm³
(d) 693 cm³
Solution:
When rolled along length, circumference = 44 cm, height = 18 cm
Circumference = 2πr = 44
2 × (22/7) × r = 44
r = 44 × 7 ÷ 44 = 7 cm
Volume = πr²h = (22/7) × 7² × 18
V = (22/7) × 49 × 18 = 22 × 7 × 18 = 2772 cm³
Answer: (a) 2772 cm³
Q50. The dimensions of a cuboid are in the ratio 5:3:2 and its total surface area is 558 cm². The volume of the cuboid is:
Options:
(a) 810 cm³
(b) 405 cm³
(c) 1620 cm³
(d) 2430 cm³
Solution:
Let dimensions be 5x, 3x, and 2x
TSA = 2(lb + bh + hl)
558 = 2[(5x)(3x) + (3x)(2x) + (2x)(5x)]
558 = 2[15x² + 6x² + 10x²]
558 = 2 × 31x² = 62x²
x² = 9, so x = 3
Dimensions: 15 cm, 9 cm, 6 cm
Volume = 15 × 9 × 6 = 810 cm³
Answer: (a) 810 cm³
Q51. Three cubes of metal whose edges are 6 cm, 8 cm, and 10 cm respectively are melted to form a single cube. The edge of the new cube is:
Options:
(a) 12 cm
(b) 24 cm
(c) 18 cm
(d) 15 cm
Solution:
Volume of first cube = 6³ = 216 cm³
Volume of second cube = 8³ = 512 cm³
Volume of third cube = 10³ = 1000 cm³
Total volume = 216 + 512 + 1000 = 1728 cm³
Edge of new cube = ∛1728 = 12 cm
Answer: (a) 12 cm
Q52. A river 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in a minute?
Options:
(a) 4000 m³
(b) 2000 m³
(c) 6000 m³
(d) 8000 m³
Solution:
Speed = 2 km/h = 2000 m/h
Distance covered in 1 minute = 2000 ÷ 60 = 100/3 m
Volume = Area of cross-section × Distance
Volume = (3 × 40) × (100/3) = 120 × (100/3) = 4000 m³
Answer: (a) 4000 m³
Q53. A solid cube is cut into two cuboids of equal volumes. The ratio of the total surface area of one cuboid to that of the cube is:
Options:
(a) 1:1
(b) 2:3
(c) 3:4
(d) 4:3
Solution:
Let the cube have side 'a'
TSA of cube = 6a²
When cut into two equal cuboids, dimensions of each cuboid = a × a × (a/2)
TSA of one cuboid = 2[a × a + a × (a/2) + (a/2) × a]
= 2[a² + a²/2 + a²/2] = 2[2a²] = 4a²
Ratio = 4a² : 6a² = 4 : 6 = 2 : 3
Answer: (b) 2:3
Q54. The height of a cylinder is increased by 100%. By what percent should its radius be decreased so that its volume remains unchanged?
Options:
(a) 50%
(b) 29.3%
(c) 70.7%
(d) 25%
Solution:
Original volume = πr²h
Height increased by 100%, so new height = 2h
Let new radius = r'
New volume = π(r')²(2h)
For volume to remain same: πr²h = π(r')²(2h)
r² = 2(r')²
(r')² = r²/2
r' = r/√2 = 0.707r
Decrease = r - 0.707r = 0.293r
Percentage decrease = (0.293r/r) × 100 = 29.3%
Answer: (b) 29.3%
Q55. The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm³. The radius of the cylinder is: (Take π = 22/7)
Options:
(a) 5 cm
(b) 3.5 cm
(c) 7 cm
(d) 2.5 cm
Solution:
Let radius = 5x and height = 7x
Volume = πr²h
550 = (22/7) × (5x)² × 7x
550 = (22/7) × 25x² × 7x
550 = 22 × 25x³
550 = 550x³
x³ = 1, so x = 1
Radius = 5x = 5 × 1 = 5 cm
Answer: (a) 5 cm
Q56. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by: (Take π = 22/7)
Options:
(a) 2.25 cm
(b) 3 cm
(c) 4 cm
(d) 1.5 cm
Solution:
Volume of sphere = (4/3)πr³ = (4/3) × π × 3³ = 36π cm³
This volume equals the volume of water displaced (cylinder)
Volume of cylinder = πR²h, where R = 4 cm
36π = π × 4² × h
36π = 16π × h
h = 36/16 = 2.25 cm
Answer: (a) 2.25 cm
Q57. The total surface area of a cube is 96 cm². The volume of the cube is:
Options:
(a) 8 cm³
(b) 27 cm³
(c) 64 cm³
(d) 512 cm³
Solution:
TSA of cube = 6a² = 96
a² = 16
a = 4 cm
Volume = a³ = 4³ = 64 cm³
Answer: (c) 64 cm³
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Lateral Surface Area (LSA) (or Curved Surface Area, CSA, for cylinders) is the area of only the sides of a 3D shape. Think of it as the area of the "four walls" of a room.
Total Surface Area (TSA) is the LSA plus the area of the top and bottom surfaces. For the room example, this would be the area of the four walls plus the area of the ceiling and the floor.
This is a common point of confusion! Here’s a simple guide:
The most important conversion to remember is: 1 m³ = 1000 Litres.
While all formulas in the chapter are important, you absolutely must know:
Area = 1/2 × (sum of parallel sides) × heightVolume = πr²hTSA = 2(lb + bh + hl)These MCQs are an excellent tool to test your knowledge, practice speed, and find your weak spots. To score full marks, you should use these MCQs after you have thoroughly practiced the NCERT textbook exercises and solved different types of word problems. Think of this as your final revision and self-test!