A field is in the from 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 meter. Then, the field is to be thoroughly ploughed at the cost of Rs. $0.50$ per $c m^{2}$ ; What is the amount required to plough the field ? [Take $π$ = $\frac{22}{7}$ ].

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Solution

$\Rightarrow$ Here, $R s .2640$ is the cost of fencing.

$\Rightarrow$ Thus, $P e r i m e t e r = \frac{T o t a l c o s t}{R a t e p e r m e t e r c o s t} = \frac{2640}{12} = 220 m$

$\Rightarrow$ Let $r$ be the radius of the field.

$\Rightarrow$ Now, $p e r i m e t e r = 2 π r$

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

$∴$ $r = 35 m$

$\Rightarrow$ Area of field $= π r^{2}$

$∴$ Area of field $= \frac{22}{7} \times 35 \times 35 = 3850 m^{2}$

$\Rightarrow$ The amount required to plough the field $= R s .0 .50 \times 3850 = R s .1925$

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A field is in the from 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 meter. Then, the field is to be thoroughly ploughed at the cost of Rs. 0.50 per cm2; What is the amount required to plough the field ? [Take π = 227].