A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be Rs. 2640 at the rate of Rs. 12 per metre. Then, the field is to be thoroughly ploughed at the cost of Rs. 0.50 per $m^2$. What is the amount required to plough the field? (Take $\pi = \frac{22}{7}$)

Given:

A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be Rs. 2640 at the rate of Rs. 12 per metre. Then, the field is to be thoroughly ploughed at the cost of Rs. 0.50 per $m^2$. 

To do:

We have to find the amount required to plough the field.

Solution:

Cost of fencing the circular field $= Rs.\ 2640$

Rate of fencing $= Rs.\ 12$ per metre.

Circumference of the circular field $=\frac{2640}{12}$

$= 220\ m$
Let $r$ be the radius of the field.

This implies,

$2\pi r = 220$

$\Rightarrow \frac{2 \times 22}{7} r=220$

$\Rightarrow r=\frac{220 \times 7}{2 \times 22}$

$\Rightarrow r=35 \mathrm{~m}$
Area of the field $=\pi r^{2}$

$=\frac{22}{7} \times(35)^{2} \mathrm{~m}^{2}$

$=\frac{22}{7} \times 35 \times 35 \mathrm{~m}^{2}$

$=3850 \mathrm{~m}^{2}$

Rate of ploughing the field $=Rs.\ 0.50$ per $\mathrm{m}^{2}$

Therefore,

Total cost of fencing $=Rs.\ 3850 \times 0.50$

$=Rs.\ 1925$

The amount required to plough the field is Rs. 1925.

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Updated on: 10-Oct-2022

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