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Class 8 Mensuration — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Find the area of a trapezium with parallel sides 10 cm and 6 cm, height 5 cm.
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Answer: A) 40 cm²
A = ½ × (10 + 6) × 5 = ½ × 16 × 5 = 40 cm².
2. Which formula gives the TOTAL surface area of a cylinder?
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Answer: C) 2πr(r + h)
TSA of cylinder = curved surface + two circular ends = 2πrh + 2πr² = 2πr(r + h).
3. An open cuboidal box (no top) measures 10 cm × 8 cm × 5 cm. Find the area of cardboard needed to make it (5 faces only).
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Answer: C) 260
TSA = 2(lb + bh + hl) = 2(80 + 40 + 50) = 340 cm². Remove one top face (l × b = 10 × 8 = 80 cm²): 340 − 80 = 260 cm².
4. A cylindrical water tank that is open at the top has radius 7 m and height 4 m. Its curved surface and its base are to be painted. Find the area to be painted. Use π = .
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Answer: B) 330 m²
Curved surface = 2πrh = 2 × × 7 × 4 = 176 m². Base circle = πr² = × 49 = 154 m². Total = 176 + 154 = 330 m². Trap 176 m²: the curved part only, forgetting the base. Trap 484 m²: the closed TSA 2πr(r + h), which counts a top the tank does not have. Trap 154 m²: the base only.
5. A garden roller has a diameter of 84 cm and a length of 120 cm. How much ground does it level in 500 complete revolutions? Give the answer in square metres. Use π = .
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Answer: B) 1584 m²
Radius = 84 ÷ 2 = 42 cm. One revolution levels the curved surface: 2πrh = 2 × × 42 × 120 = 31,680 cm². In 500 revolutions: 15,840,000 cm². Since 1 m² = 10,000 cm², that is 1584 m². Trap 3168 m²: putting the diameter 84 cm into the radius slot, which doubles the answer. Trap 15,840 m²: dividing by 1000 instead of 10,000. Trap 158.4 m²: dividing by 100,000.
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