A 30 m chain used for a survey was found to be 30.10 m at the beginning and 30.30 m at the end of the work. The area of the plan drawn to a scale of 1 cm = 8 m was measured with the help of a planimeter and was found to be 42.50 sq. cm. What is the true area of the field?
Option 1: 2890.9 m2
Option 2: 2567.0 m2
Option 3: 3456.4 m2
Option 4: 2756.4 m2
Correct Answer
Option 4: 2754.4 m2
Solution For A 30 m chain used for a survey was found to be 30.10 m
Concept Behind this solution
True Area = (L'/L)2 * Measured Area
Where'
L' = actual length of the chain while measuring distance = Average length of the chain while measuring
L = true length of chain
Calculation:
Data Given is:
- L'1 = 30.10 m,
- L'2 = 8 m,
- L = 30 m,
- Scale = 1cm:8m
- Area of Plan = 42.50 sq.cm.
Now Here Area of Field = 42.50 x 82 = 2720 sq. m.
We know that L' = (L'1+L'2)/2
L' = (30.10 + 30.30)/2
L' = 30.20 m
We know that, True Area = (L'/L)2 * Measured Area
True Area = (30.20/30)2 * 2720
True Area of Field = 2756.4 m2
