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. [tex]\large\underline{\sf{Given- }}[/tex]

   • The area of a circle is 13.86 hectares .

   • The cost of fencing is 60 paisa per meter.

   [tex]\large\underline{\sf{To\:Find – }}[/tex]

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

   [tex]\begin{gathered}\Large{\sf{{\underline{Formula \: Used – }}}} \end{gathered}[/tex]

   [tex] 1. \: \: \: \boxed{ \sf \: Area_{(circle)} = \pi \: {r}^{2} }[/tex]

   [tex] 2. \: \: \: \boxed{ \sf \: Perimeter_{(circle)} = 2\pi \: r}[/tex]

   [tex] 3. \: \: \: \boxed{ \sf \: 1 \: hectare = 10000 \: {m}^{2} }[/tex]

   [tex]\large\underline{\sf{Solution-}}[/tex]

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

   Given that

   [tex]\rm :\longmapsto\:Area_{(circle)} = 13.86 \: hectare \: [/tex]

   [tex]\rm :\longmapsto\:\pi \: {r}^{2} = 13.86 \times 10000 \: {m}^{2} [/tex]

   [tex]\rm :\longmapsto\:\dfrac{22}{7} \times {r}^{2} = 138600[/tex]

   [tex]\rm :\longmapsto\: {r}^{2} = 6300 \times 7[/tex]

   [tex]\rm :\longmapsto\:r = \sqrt{3 \times 3 \times 7 \times 100 \times 7} [/tex]

   [tex]\bf\implies \:r = 210 \: m[/tex]

   Now,

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

   We have,

   • Radius of circle, r = 210 m

   So,

   [tex]\rm :\longmapsto\:Perimeter_{(circle)} = 2\pi \: r[/tex]

   [tex]\rm :\longmapsto\:Perimeter_{(circle)} = 2 \times \dfrac{22}{7} \times 210[/tex]

   [tex]\rm :\longmapsto\:Perimeter_{(circle)} = 1320 \: m[/tex]

   Now,

   [tex]\rm :\longmapsto\:Cost \: of \: fencing \: 1 \: m \: = \: Rs \: 0.6[/tex]

   [tex]\rm :\longmapsto\:Cost \: of \:fencing \: 1320 \:m= 0.6 \times 1320 =Rs \: 792[/tex]

   Additional Information :-

   [tex] 1. \: \: \: \boxed{ \sf \: Area_{(rectangle)} = length \times breadth}[/tex]

   [tex] 2. \: \: \: \boxed{ \sf \: Perimeter_{(rectangle)} = 2(length + breadth}[/tex]

   [tex] 3. \: \: \: \boxed{ \sf \: Area_{(square)} = {(side)}^{2} }[/tex]

   [tex] 4. \: \: \: \boxed{ \sf \: Perimeter_{(square)} = 4 \times side}[/tex]

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