Section 4: Soil and Water Conservation Engineering
Surveying and Levelling
Subtopic: Measurement of distance and area
Question Statement:
The area of a map plotted to a scale of 1:3000 measures 9069.37 mm². The 20 m chain used for this survey was short by 0.2 m. The true land area it represents is
Options:
(A) 83281 m²
(B) 82449 m²
(C) 80808 m²
(D) 80000 m²
Official Answer Key:
D
Step-by-Step Solution & Explanation
Nominal ground area = plotted area × (scale)² converted to m² = 9069.37 mm² × (3000/1000)² m²/mm² = 9069.37 × 9 = 81624.3 m². Since the chain was actually only 19.8 m (short by 0.2 m), every ground distance measured was overstated in the ratio 20/19.8; the true area correction factor is (19.8/20)² = 0.9801. True area = 81624.3 × 0.9801 ≈ 80000 m².
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