Capacity of a canal with isosceles trapezium cross-section: Cross-section is an isosceles trapezium, 3 m wide at bottom and 5 m at top, depth 2 m, length 110 m. Find the maximum capacity (in cubic metres).
Aptitude
Area
Difficulty: Easy
Choose an option
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A1760 cubic metres
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B1650 cubic metres
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C1056 cubic metres
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D880 cubic metres
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E990 cubic metres
Answer
Correct Answer: 880 cubic metres
Explanation
Introduction / Context:The canal’s capacity equals cross-sectional area times length. The cross-section is a trapezium with known parallel sides and height (depth).
Given Data / Assumptions:
- Bottom width b1 = 3 m; top width b2 = 5 m.
- Depth h = 2 m.
- Length L = 110 m.
Concept / Approach:Area(trapezium) = (1/2) * (b1 + b2) * h. Capacity = Area * L.
Step-by-Step Solution:
Area = (1/2) * (3 + 5) * 2 = 8 m^2.Capacity = 8 * 110 = 880 m^3.Verification / Alternative check:Units: (m^2)*m → m^3, correct.
Why Other Options Are Wrong:1760, 1650, 1056, 990 do not equal 8*110.
Common Pitfalls:Using the average width incorrectly or forgetting to multiply by the length.
Final Answer:880 cubic metres