Question

The cost of fencing a circular field at the rate of ₹ 24 per metre is ₹ 5280.

Calculate: 

1. the radius of the field. 
2. the cost of ploughing the field at the rate of ₹ 2 per m².

Answer 1

Given:

• Cost of fencing = ₹ 5280
• Rate of fencing = ₹ 24 per metre
• Cost of ploughing = ₹ 2 per m²

Step-wise calculation:

i. Find the radius of the circular field:

Cost of fencing = Perimeter (Circumference) × Rate per metre

₹ 5280 = Circumference × ₹ 24

Circumference = `5280/24` = 220 metres

We know, circumference of circle (C = 2πr)

Assuming `π = 22/7`,

`2 xx 22/7 xx r = 220`

`44/7 xx r = 220`

`r = (220 xx 7)/44`

r = 35 metres 

ii. Calculate the cost of ploughing the field:

Area of circle 

`A = πr^2`

= `22/7 xx 35^2`

`A = 22/7 xx 1225`

A = 3850 m²

Cost of ploughing

= Area × Cost per m² 

= 3850 × 2

= ₹ 7700

The radius of the field is 35 metres. 

The cost of ploughing the field is ₹ 7700.