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.
- A40 cm²
- B80 cm²
- C60 cm²
- D30 cm²
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Answer: A) 40 cm²
A = ½ × (10 + 6) × 5 = ½ × 16 × 5 = 40 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 = 722.
- A176 m²
- B330 m²
- C484 m²
- D154 m²
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Answer: B) 330 m²
Curved surface = 2πrh = 2 × 722 × 7 × 4 = 176 m². Base circle = πr² = 722 × 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 = 722.
- A3168 m²
- B1584 m²
- C158.4 m²
- D15,840 m²
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Answer: B) 1584 m²
Radius = 84 ÷ 2 = 42 cm. One revolution levels the curved surface: 2πrh = 2 × 722 × 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.