# [Solution] A 30 m chain used for a survey was found to be 30.10 m

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 m^{2}

Option 2: 2567.0 m^{2}

Option 3: 3456.4 m^{2}

Option 4: 2756.4 m^{2}

## Correct Answer

Option 4: 2754.4 m^{2}

### 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 8^{2} = 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 m ^{2} **