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 planimeter and was found to be 42.50 sq. cm. What is true area of the field?

This question was previously asked in

DFCCIL Executive Civil 2018 Official Paper

Option 3 : 2756.4 m^{2}

CT 1: Current Affairs (Government Policies and Schemes)

55064

10 Questions
10 Marks
10 Mins

**Concept:**

**\(\text{True area} = (\frac{L'}{L})^2 × \text{measured area}\)**

Where,

L' = actual length of the chain while measuring distance = Average length of the chain while measuring,

L = true length of chain,

**Calculation:**

Given,

L'_{1} = 30.10 m, L'_{2} = 30.30 m, L = 30 m,

Scale = 1 cm : 8 m, area of plan = 42.50 sq. cm.

Now, Area of field = 42.50 × 8^{2} = 2720 sq. m.

∵ We know that, \(\text{L'} = \frac{L'_1 + L'_2}{2}\)

⇒ \(\text{L'} = \frac{30.10 + 30.30}{2}\)

∴ L' = 30.20 m

∵ We know that, \(\text{True area} = (\frac{L'}{L})^2 × \text{measured area}\)

⇒ \(\text{True area} = (\frac{30.2}{30})^2 × \text{2720}\)

∴ **True Area of field = 2756.4 m ^{2}**