Estimating Corrected Area from Map of Shrunk Factor ‘F’

The corrected area is the real area of a land or region, which needs to be estimated from a map. The map is created by reducing the actual size of the land to fit into a sheet of paper or screen. This reduction is called the shrunk factor ‘F’. The corrected area is estimated by multiplying the area shown on the map by a correction factor.

The correction factor is calculated by using the shrunk factor ‘F’. The corrected area is directly proportional to the square of the shrunk factor ‘F’. Therefore, the correct answer is option B.

Explanation of Options

Let’s understand why option B is the correct answer:

Option A: It is directly proportional to F.

If the corrected area is directly proportional to the shrunk factor ‘F’, then it means that the corrected area will increase or decrease linearly with the increase or decrease in ‘F’. However, this is not correct because the corrected area is not a linear function of the shrunk factor ‘F’. Therefore, option A is incorrect.

Option B: It is directly proportional to the e square of F.

The corrected area is directly proportional to the square of the shrunk factor ‘F’. The square of ‘F’ is denoted by ‘F²’, and it is a non-linear function of ‘F’. Therefore, option B is correct.

Option C: It is inversely proportional to F.

If the corrected area is inversely proportional to the shrunk factor ‘F’, then it means that the corrected area will decrease linearly with the increase in ‘F’. However, this is not correct because the corrected area is not a linear function of the shrunk factor ‘F’. Therefore, option C is incorrect.

Option D: It is inversely proportional to square of F.

If the corrected area is inversely proportional to the square of the shrunk factor ‘F’, then it means that the corrected area will decrease non-linearly with the increase in ‘F’. However, this is not correct because the corrected area is directly proportional to the square of the shrunk factor ‘F’. Therefore, option D is incorrect.

Conclusion

The corrected area is estimated by multiplying the area shown on the map by a correction factor. The correction factor is calculated by using the shrunk factor ‘F’. The corrected area is directly proportional to the square of the shrunk factor ‘F’. Therefore, option B is the correct answer.