Question

The circumference of a circle is 4pi Find the area of the circle.
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Answer 1

Given that , The circumference of a circle is 4$\pi$ units .

Need To Find : Area of Circle ?

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Radius of Circle to find Area of Circle :

❍ Let's Consider Radius of Circle be r .

As , We know that ,

• Formula for Circumference of Circle :

$\qquad \star \:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Circumference _{(\:Circle \:)} \:=\: 2\pi r \:\:units\:}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Here , r is the Radius of Circle, Circumference of Circle is 4$\pi$ units & $\sf \pi \:=\:\dfrac{22}{7}$ .

$\dashrightarrow \sf \:\:Circumference _{(\:Circle \:)} \:=\: 2\pi r$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\dashrightarrow \sf \:\:Circumference _{(\:Circle \:)} \:=\: 2\pi r \\\\ \dashrightarrow \sf \:\:4 \pi \:=\: 2\pi r \\\\\dashrightarrow \sf \:\:\dfrac{4 \pi }{2 \pi } \:=\: r \\\\\dashrightarrow \sf \:\:\cancel {\dfrac{4 \pi }{2 \pi }} \:=\: r \\\\\dashrightarrow \sf \:\:2 \:=\: r \\\\\dashrightarrow \sf \: r \:\:=\:2 \: \\\\ \dashrightarrow \underline {\boxed {\pmb{\purple {\frak{ \:\:r \:(\:or \:Radius \:)\:=\: 2 \:units \:}}}}}$

• Radius of Circle is 2 units .

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Area of Circle :

As , We know that ,

• Formula for Area of Circle :

$\qquad \star \:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Area _{(\:Circle \:)} \:=\: \pi \:(r)^2 \:\:sq.units\:}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Here , r is the Radius of Circle, & $\sf \pi \:=\:\dfrac{22}{7}$ .

$\dashrightarrow \sf \:\:Area _{(\:Circle \:)} \:=\: \pi \:(r)^2 \:\:sq.units \:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\dashrightarrow \sf \:\:Area _{(\:Circle \:)} \:=\: \pi \:(r)^2 \\\\ \dashrightarrow \sf \:\:Area_{(\:Circle \:)} \:=\: \pi (2)^2 \\\\\dashrightarrow \sf \:\:Area_{(\:Circle \:)} \:=\: \pi 4 \\\\\dashrightarrow \sf \:\:Area_{(\:Circle \:)} \:=\: 4\pi \\\\\dashrightarrow \underline {\boxed {\pmb{\purple {\frak{ \:\:\:\:Area _{(\:Circle \:)} \:\:=\: 4\pi \:sq.units \:}}}}}$

$\qquad \therefore \underline {\sf Hence, \:The \:Area \:of \:Circle \:is \:\pmb{\bf {4 \pi \:sq.units}} \:}$