Mensuration: Areas, Surface Areas and Volumes MCQs

Solved quantitative aptitude MCQs on the perimeter and area of plane figures and the surface area and volume of cuboids, cubes, cylinders, cones and spheres, with formulas.

1. 1

   A rectangular park is 18 m long and 12 m wide. What is its perimeter?

   A60 mB66 mC72 mD216 m

   Correct answer: A. 60 m

   Perimeter = 2 × (length + breadth) = 2 × 30 = 60 m.

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2. 2

   The diagonal of a square is 12 cm. What is its area?

   A65 cm²B72 cm²C79 cm²D86 cm²

   Correct answer: B. 72 cm²

   Area of a square = (diagonal)² ÷ 2 = 144 ÷ 2 = 72 cm².

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3. 3

   Find the area of a trapezium whose parallel sides are 10 cm and 16 cm and whose height is 8 cm.

   A84 cm²B94 cm²C104 cm²D114 cm²

   Correct answer: C. 104 cm²

   Area = ½ × (sum of parallel sides) × height = ½ × 26 × 8 = 104 cm².

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4. 4

   The diagonals of a rhombus are 12 cm and 16 cm. What is its area?

   A28 cm²B48 cm²C86 cm²D96 cm²

   Correct answer: D. 96 cm²

   Area of a rhombus = ½ × d₁ × d₂ = ½ × 12 × 16 = 96 cm².

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5. 5

   The diagonals of a rhombus are 12 cm and 16 cm. What is the length of each side?

   A10 cmB11 cmC14 cmD20 cm

   Correct answer: A. 10 cm

   The diagonals bisect each other at right angles, so each side = √(6² + 8²) = √100 = 10 cm.

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6. 6

   Find the area of a triangle whose sides are 13 cm, 14 cm and 15 cm.

   A76 cm²B84 cm²C91 cm²D92 cm²

   Correct answer: B. 84 cm²

   By Heron's formula, s = (13 + 14 + 15) ÷ 2 = 21 and area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².

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7. 7

   The area of a circle is 154 cm². What is its radius? (Take π = 22/7.)

   A5 cmB6 cmC7 cmD8 cm

   Correct answer: C. 7 cm

   πr² = 154, so r² = 154 × 7 ÷ 22 = 49 and r = 7 cm.

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8. 8

   Find the perimeter of a semicircle of radius 7 cm. (Take π = 22/7.)

   A22 cmB29 cmC32 cmD36 cm

   Correct answer: D. 36 cm

   Perimeter of a semicircle = πr + 2r = 22 + 14 = 36 cm (the curved part plus the diameter).

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9. 9

   A wheel of radius 35 cm rolls without slipping. How many revolutions will it make in covering 2.2 km? (Take π = 22/7.)

   A1,000B1,100C1,200D2,000

   Correct answer: A. 1,000

   Circumference = 2 × 22/7 × 35 = 220 cm. 2.2 km = 2,20,000 cm, so revolutions = 2,20,000 ÷ 220 = 1,000.

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10. 10

    Find the volume of a cuboid 12 cm long, 8 cm wide and 5 cm high.

    A432 cm³B480 cm³C528 cm³D576 cm³

    Correct answer: B. 480 cm³

    Volume = length × breadth × height = 12 × 8 × 5 = 480 cm³.

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12. 11

    Find the total surface area of a cuboid 12 cm long, 8 cm wide and 5 cm high.

    A200 cm²B353 cm²C392 cm²D431 cm²

    Correct answer: C. 392 cm²

    Total surface area = 2(lb + bh + hl) = 2(96 + 40 + 60) = 392 cm².

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13. 12

    What is the length of the diagonal of a cube of side 6 cm?

    A6 cmB6√2 cmC6√3 cmD12 cm

    Correct answer: C. 6√3 cm

    The diagonal of a cube = side × √3 = 6√3 cm. (The diagonal of one face would be 6√2 cm.)

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14. 13

    Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7.)

    A440 cm²B484 cm²C748 cm²D1,540 cm²

    Correct answer: A. 440 cm²

    Curved surface area = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².

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15. 14

    Find the volume of a cone of radius 7 cm and height 12 cm. (Take π = 22/7.)

    A554 cm³B616 cm³C678 cm³D924 cm³

    Correct answer: B. 616 cm³

    Volume = ⅓πr²h = ⅓ × 22/7 × 49 × 12 = 616 cm³. (A cylinder of the same size would hold 1,848 cm³, three times as much.)

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16. 15

    A cone has radius 6 cm and height 8 cm. What is its slant height?

    A8 cmB9 cmC10 cmD11 cm

    Correct answer: C. 10 cm

    Slant height l = √(r² + h²) = √(36 + 64) = 10 cm.

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17. 16

    Find the volume of a sphere of radius 21 cm. (Take π = 22/7.)

    A5,544 cm³B19,404 cm³C29,106 cm³D38,808 cm³

    Correct answer: D. 38,808 cm³

    Volume = 4/3 πr³ = 4/3 × 22/7 × 9,261 = 38,808 cm³.

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18. 17

    Find the surface area of a sphere of radius 7 cm. (Take π = 22/7.)

    A616 cm²B678 cm²C740 cm²D1,437 cm²

    Correct answer: A. 616 cm²

    Surface area = 4πr² = 4 × 22/7 × 49 = 616 cm².

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19. 18

    Find the total surface area of a solid hemisphere of radius 7 cm. (Take π = 22/7.)

    A416 cm²B462 cm²C508 cm²D554 cm²

    Correct answer: B. 462 cm²

    Total surface area = curved part (2πr²) + flat circle (πr²) = 3πr² = 3 × 154 = 462 cm².

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20. 19

    A room is 10 m long, 8 m wide and 4 m high. What is the area of its four walls?

    A116 m²B130 m²C144 m²D158 m²

    Correct answer: C. 144 m²

    Area of four walls = 2 × height × (length + breadth) = 2 × 4 × 18 = 144 m².

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21. 20

    If the radius of a circle is doubled, its area becomes:

    Athe sameBtwo timesCfour timesDeight times

    Correct answer: C. four times

    Area = πr². Doubling r makes r² four times as large, so the area is 4 times.

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