Surface Measure Conversions: Identifying the Incorrect Statement

This question requires identifying the incorrect statement among the given conversion factors for 1 Square mile. We will verify each option.

Verification of Surface Measure Conversions

• Option 1: 1 Sq. mile = 2.590 Sq. kilometres
  A mile is approximately 1.60934 kilometres. Squaring this gives:
  $1 \text{ Sq. mile} = (1.60934 \text{ km})^2 \approx 2.589988 \text{ Sq. km}$
  Rounded to three decimal places, this is 2.590 Sq. km. Thus, this statement is correct.
• Option 2: 1 Sq. mile = 259 Hectares
  Since 1 Sq. km equals 100 Hectares, and we know 1 Sq. mile is approximately 2.590 Sq. km:
  $1 \text{ Sq. mile} \approx 2.590 \times 100 \text{ Hectares} = 259 \text{ Hectares}$
  This statement is correct.
• Option 3: 1 Sq. mile = 640 Acres
  This is a standard and well-established conversion factor used in land measurement.
  This statement is correct.
• Option 4: 1 Sq. mile = $10^9$ Sq. centimetres
  First, convert 1 mile to centimetres:
  $1 \text{ mile} = 1.60934 \text{ km} = 1609.34 \text{ m} = 160934 \text{ cm}$
  Now, calculate the area in square centimetres:
  $1 \text{ Sq. mile} = (160934 \text{ cm})^2 = 25,899,983,742.2 \text{ Sq. cm}$
  The value $10^9$ Sq. cm is $1,000,000,000$ Sq. cm.
  Comparing the calculated value with the given value: $25,899,983,742.2 \neq 1,000,000,000$.
  Therefore, this statement is incorrect.

Final Conclusion

Based on the calculations, the statement claiming 1 Sq. mile equals $10^9$ Sq. centimetres is not correct.