Question

On a map, villages, P and Q are marked 5cm apart. The actual distance between them is 20km. What is the scale of the map? Calculate the R.F. of the map.

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Answer 1

$\huge\text{\red{✠ Given:–}}$

‎ ‎ ‎ ‎• Distance between P and Q = 5cm

‎ ‎ ‎ ‎• Actual distance between them =20km

$\huge\text{\red{✠ To find:–}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎• Relative Distance (R.F.) of map

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎• Scale of the map

$\huge\text{\red{✠ As we know:– }}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎• R.F. of the map = Distance on map / Distance on ground

$\huge\text{\red{✠ Step\:by\:step\: explaination:–}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎As we have distance on the ground so, scale of map is 5cm to 20km or 1cm to 4km.

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎Calculating the R.F. of the map...

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎That is,

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎R.F. of the map = Distance on map / Distance on ground

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ Evaluating values...

‎ ‎ ‎ ‎ ‎ ‎ ‎⟹ ‎${\dfrac{1cm}{4 \times 100000cm}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎⟹ $\dfrac{1}{400000}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎Note:–

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎1km = 1,00,000 cm

Understanding the terms:-

• Scale of a map : Maps represent the surface of the earth on a small scale on a piece of paper.

• Representative fraction : A useful and accurate method of representing the scale of a map is by a ratio or fraction called representative fraction.

• Maps : Maps are drawn to represent the earth as a whole or parts of it drawn to scale on a flat surface.