Capacity of a canal with isosceles trapezium cross-section:\nCross-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).

Difficulty: Easy

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

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