Question

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

Answer 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,

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

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

Additional Information :-

$1. \: \: \: \boxed{ \sf \: Area_{(rectangle)} = length \times breadth}$

$2. \: \: \: \boxed{ \sf \: Perimeter_{(rectangle)} = 2(length + breadth}$

$3. \: \: \: \boxed{ \sf \: Area_{(square)} = {(side)}^{2} }$

$4. \: \: \: \boxed{ \sf \: Perimeter_{(square)} = 4 \times side}$