# The area of a circle is 13.86 hectares . Find the cost of fencing it at the rate of 60 paisa per meter​

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The area of a circle is 13.86 hectares . Find the cost of fencing it at the rate of 60 paisa per meter​

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1. $$\large\underline{\sf{Given- }}$$

• The area of a circle is 13.86 hectares .
• The cost of fencing is 60 paisa per meter.

$$\large\underline{\sf{To\:Find – }}$$

• Cost of fencing the circle at Rs 0.6 per meter.

$$\begin{gathered}\Large{\sf{{\underline{Formula \: Used – }}}} \end{gathered}$$

$$1. \: \: \: \boxed{ \sf \: Area_{(circle)} = \pi \: {r}^{2} }$$

$$2. \: \: \: \boxed{ \sf \: Perimeter_{(circle)} = 2\pi \: r}$$

$$3. \: \: \: \boxed{ \sf \: 1 \: hectare = 10000 \: {m}^{2} }$$

$$\large\underline{\sf{Solution-}}$$

• Let assume that radius of circle be ‘r’ meter.

Given that

$$\rm :\longmapsto\:Area_{(circle)} = 13.86 \: hectare \:$$

$$\rm :\longmapsto\:\pi \: {r}^{2} = 13.86 \times 10000 \: {m}^{2}$$

$$\rm :\longmapsto\:\dfrac{22}{7} \times {r}^{2} = 138600$$

$$\rm :\longmapsto\: {r}^{2} = 6300 \times 7$$

$$\rm :\longmapsto\:r = \sqrt{3 \times 3 \times 7 \times 100 \times 7}$$

$$\bf\implies \:r = 210 \: m$$

Now,

To fence, around a circle, we have to find its perimeter.

We have,

• Radius of circle, r = 210 m

So,

$$\rm :\longmapsto\:Perimeter_{(circle)} = 2\pi \: r$$

$$\rm :\longmapsto\:Perimeter_{(circle)} = 2 \times \dfrac{22}{7} \times 210$$

$$\rm :\longmapsto\:Perimeter_{(circle)} = 1320 \: m$$

Now,

$$\rm :\longmapsto\:Cost \: of \: fencing \: 1 \: m \: = \: Rs \: 0.6$$

$$\rm :\longmapsto\:Cost \: of \:fencing \: 1320 \:m= 0.6 \times 1320 =Rs \: 792$$

$$1. \: \: \: \boxed{ \sf \: Area_{(rectangle)} = length \times breadth}$$
$$2. \: \: \: \boxed{ \sf \: Perimeter_{(rectangle)} = 2(length + breadth}$$
$$3. \: \: \: \boxed{ \sf \: Area_{(square)} = {(side)}^{2} }$$
$$4. \: \: \: \boxed{ \sf \: Perimeter_{(square)} = 4 \times side}$$