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An area of 64 square kilometer is represented by 256 square centimeters 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?
Verified Answer
An area of 64 square kilometer is represented by 256 square centimeter...
Representative Factor, RF is 256 cm2 = 64 cm2
Factor for measuring area is given by
Most Upvoted Answer
An area of 64 square kilometer is represented by 256 square centimeter...
Given information:
- Area on the map: 256 square centimeters
- Corresponding area in reality: 64 square kilometers
To find:
- The R. F. (Representative Fraction) of the scale
Assumptions:
- 1 kilometer = 1000 meters
- 1 meter = 100 centimeters
Approach:
- Convert the area on the map from square centimeters to square kilometers
- Use the formula for R. F. to find the scale
Calculations:
1. Convert 256 square centimeters to square kilometers:
- 1 square kilometer = (1000 meters)^2 = 1,000,000 square meters
- 1 square meter = (100 centimeters)^2 = 10,000 square centimeters
- 256 square centimeters = 256/10,000 square meters
- 256/10,000 square meters = 0.0256 square meters
- 0.0256 square meters = 0.0256/1,000,000 square kilometers
- 0.0256/1,000,000 square kilometers = 0.0000000256 square kilometers
2. Calculate the R. F. (Representative Fraction) of the scale:
- R. F. = Real distance on the ground/Distance on the map
- Real distance on the ground = 64 square kilometers
- Distance on the map = 0.0000000256 square kilometers
- R. F. = 64/0.0000000256 = 2,500,000,000
Answer:
The R. F. (Representative Fraction) of the scale is 1/50000000, which is option 'B'.
- Area on the map: 256 square centimeters
- Corresponding area in reality: 64 square kilometers
To find:
- The R. F. (Representative Fraction) of the scale
Assumptions:
- 1 kilometer = 1000 meters
- 1 meter = 100 centimeters
Approach:
- Convert the area on the map from square centimeters to square kilometers
- Use the formula for R. F. to find the scale
Calculations:
1. Convert 256 square centimeters to square kilometers:
- 1 square kilometer = (1000 meters)^2 = 1,000,000 square meters
- 1 square meter = (100 centimeters)^2 = 10,000 square centimeters
- 256 square centimeters = 256/10,000 square meters
- 256/10,000 square meters = 0.0256 square meters
- 0.0256 square meters = 0.0256/1,000,000 square kilometers
- 0.0256/1,000,000 square kilometers = 0.0000000256 square kilometers
2. Calculate the R. F. (Representative Fraction) of the scale:
- R. F. = Real distance on the ground/Distance on the map
- Real distance on the ground = 64 square kilometers
- Distance on the map = 0.0000000256 square kilometers
- R. F. = 64/0.0000000256 = 2,500,000,000
Answer:
The R. F. (Representative Fraction) of the scale is 1/50000000, which is option 'B'.
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