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An area of 64 square kilometre is represented by 256 square centimetres on a map. The R. F. of the scale is
- a)1/4
- b)1/50000
- c)1/2
- d)1/5000
Correct answer is option 'B'. Can you explain this answer?
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An area of 64 square kilometre is represented by 256 square centimetr...
Representative Factor, RF is 256 cm2 = 64 cm2
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Factor for measuring area is given by
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An area of 64 square kilometre is represented by 256 square centimetr...
Understanding the Problem
To find the Representative Fraction (R.F.) of the scale, we need to relate the real area to the area represented on the map.
Given Data
- Real area = 64 square kilometres
- Area on map = 256 square centimetres
Conversion of Units
1 square kilometre = 1,000,000 square metres
1 square metre = 10,000 square centimetres
Thus,
1 square kilometre = 10,000,000,000 square centimetres
Calculating Real Area in Square Centimetres
64 square kilometres = 64 x 10,000,000,000 square centimetres
= 640,000,000,000 square centimetres
Finding the R.F.
The formula for the Representative Fraction (R.F.) is:
R.F. = (Area on map) / (Real area in same units)
Substituting the values:
R.F. = 256 cm² / 640,000,000,000 cm²
= 256 / 640,000,000,000
= 1 / (640,000,000,000 / 256)
= 1 / 2,500,000
= 1 / 50,000
Conclusion
Therefore, the R.F. of the scale is 1/50000, which corresponds to option B. This means that 1 unit on the map equals 50,000 units in reality.
To find the Representative Fraction (R.F.) of the scale, we need to relate the real area to the area represented on the map.
Given Data
- Real area = 64 square kilometres
- Area on map = 256 square centimetres
Conversion of Units
1 square kilometre = 1,000,000 square metres
1 square metre = 10,000 square centimetres
Thus,
1 square kilometre = 10,000,000,000 square centimetres
Calculating Real Area in Square Centimetres
64 square kilometres = 64 x 10,000,000,000 square centimetres
= 640,000,000,000 square centimetres
Finding the R.F.
The formula for the Representative Fraction (R.F.) is:
R.F. = (Area on map) / (Real area in same units)
Substituting the values:
R.F. = 256 cm² / 640,000,000,000 cm²
= 256 / 640,000,000,000
= 1 / (640,000,000,000 / 256)
= 1 / 2,500,000
= 1 / 50,000
Conclusion
Therefore, the R.F. of the scale is 1/50000, which corresponds to option B. This means that 1 unit on the map equals 50,000 units in reality.
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