A Plot of land measures 30 cm x 60 cm on a map drawn to scale 1 cm = 50 m. What will be the area of the map when placed on a topographical map drawn to a scale of 1 cm = 600 m?

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JKSSB JE CE 2015 Official Paper

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Answer 1

Given : -

Area of land on map, a = 30cm x 60 cm = 1800cm²

Scale of map, S₁ = 1/5000

Scale of topographical map, S₂ = 1/60000

Solution: -

Actual area of land,

\({A_{actual}} = \frac{a}{{S_1^2}} = \left( {1800 \times {{5000}^2}} \right)\)

Area of land on topographical map,

\({a_2} = {A_{actual}} \times S_2^2\)

⇒ \([{a_2} = \left( {1800 \times {{5000}^2}} \right) \times {\left( {\frac{1}{{60000}}} \right)^2} = 12.5\;c{m^2}\)