Question
1. Surface calculation. Comment on how you would solve this case. A rectangular plot of land has a surface area of 9 cm2 on a scale of 1:25,000. Calculate the actual surface area in m2 and km2.
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Answer to a math question 1. Surface calculation. Comment on how you would solve this case. A rectangular plot of land has a surface area of 9 cm2 on a scale of 1:25,000. Calculate the actual surface area in m2 and km2.
Nash
4.987 Answers
1. Determine the scale factor from the given scale \(1:25,000\):
\text{Scale factor} = 25000
2. Compute the real area from the given scaled area:
A_{real} = 9 \, \text{cm}^2 \times (25000)^2
3. Convert the area to \(\text{m}^2\) (knowing that \(1 \, \text{cm}^2 = 0.0001 \, m^2\)):
A_{real} = 9 \times 625000000 \, \text{cm}^2
A_{real} = 5625000000 \, \text{cm}^2
A_{real} = 562500 \, \text{m}^2
4. Convert the area to \(\text{km}^2\) (knowing that \(1 \, \text{km}^2 = 1000000 \, m^2\)):
A_{real} = \frac{562500}{1000000} \, \text{km}^2
A_{real} = 0.5625 \, \text{km}^2
The real area is:
A = 562500 \, \text{m}^2 = 0.5625 \, \text{km}^2
2. Compute the real area from the given scaled area:
3. Convert the area to \(\text{m}^2\) (knowing that \(1 \, \text{cm}^2 = 0.0001 \, m^2\)):
4. Convert the area to \(\text{km}^2\) (knowing that \(1 \, \text{km}^2 = 1000000 \, m^2\)):
The real area is:
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