A canal's trapezoidal cross-section has a 10 m top width, 6 m bottom width, and a 640 sq m area. Find the canal depth_________?
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Answer: D. 80 m
Explanation
The area of a trapezoidal cross-section equals one-half times the sum of the parallel top and bottom widths times depth. Substituting the given values gives six hundred forty equals one-half times ten plus six times depth. Simplifying the equation gives six hundred forty equals eight times depth, solving to an eighty meter depth. Trapezoid area is calculated using the average of its two parallel base lengths multiplied by its height. Canal cross-sections are often modeled as trapezoids to reflect natural sloping riverbank excavation profiles. Solving linear equations for depth requires isolating the unknown variable by dividing both sides.
Civil engineers calculate canal and trench cross-sectional areas to estimate excavation and earthmoving volumes. Hydrologists use trapezoidal channel dimensions to determine water flow rates and irrigation capacity. Practical geometry applications bridge mathematical formulas with civil engineering design work. Option A underestimates the canal depth by miscalculating the parallel side width sum multiplier. Option B results from an arithmetic error during the final division step of the trapezoid formula. Option D is the correct answer, representing an eighty meter canal depth calculation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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