Question

★Question : -

a wire in the form of square with side 22cm. it is reshaped and bent into the form of circle. calculate the area of this circle.​

Answer 1

${ \large{ \underline{ \pmb{ \rm{ \circ \: Given ...}}}}}$

➼ a wire in the form of square with side 22cm.

➼ is reshaped and bent into the form of circle.

${ \large{ \underline{ \pmb{ \rm{ \circ \: To \: Find ...}}}}}$

➼ calculate the area of this circle.

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Understanding \: the \: Concept }}}}}$

● Here, it is said that a wire is bent to form a square of the side 22cm and then again rebent to form a circle so, which means we can state that the length of wire used for making a square = length of wire used for making the circle. which is nothing but perimeter of the square equals perimeter of the circle

❍ So,now we have to find the perimeter of the square as we know the perimeter of the square and the circle are the same. then we should find the radius of the circle to find its area with the help of the perimeter.

${ \large{ \underline{ \pmb{ \rm{ \circ \: Solution...}}}}}$

★ Area of the circle is 616cm² respectively!

${ \large{ \underline{ \pmb{ \sf{ \circ \: Full \: Solution ...}}}}}$

➱ Now,

• ↝Let's firstly find the perimeter of the square.

➱ Here,

• ↠Side of the square = 4 × side

➼ Formula : -

$\circ \:{ \pink { \boxed{ \rm { Perimeter\: of \: a \: Square = 4 \times side}} \star}}$

● Substituting the values,

${ : \implies} \rm \:Perimeter _{(square)} = 4 \times Side \: \: \\ \\ \\ { : \implies} \rm \:Perimeter _{(square)} = 4 \times 22cm \\ \\ \\ { : \implies} \rm \:Perimeter _{(square)} = { \pink{ \boxed{ \frak{88cm}} \star}} \: \: \:$

• Henceforth, the perimeter of the square is 88cm~

↝ We know that,

$\star \: {\blue{ \underline{ \boxed{ \pink{ \mathfrak{ perimeter_{(square)} = perimeter_{(circle) }}}}}}}$

• Henceforth the perimeter of the circle is 88cm

➱ Now,

• Let's find the radius of the circle to find the area of the circle

➼ Formula : -

$\circ \:{ \pink { \boxed{ \rm { Perimeter\: of \: a \: circle = 2\pi \: r}} \star}}$

➱ Here,

• Perimeter of the circle = 88cm
• Pi = 22/7

↠Substituting we get,

${ : \implies} \rm \:Perimeter _{(circle)} = 2\pi \: r \\ \\ \\{ : \implies} \rm 88 cm = 2 \times \frac{22}{7} \times r \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: 88cm = \frac{44}{7} \times r \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: r = \frac{88 \times 7}{44} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: r = \frac{616}{44} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: r ={ \pink{ \boxed{ \frak{ 14cm}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the radius of the circle is 14cm

➱ Now,

• Let's find the area of the circle

➼ Formula : -

$\circ \:{ \pink { \boxed{ \rm {\: Are \: of \: a \: circle = \pi \: {r}^{2} }} \star}}$

➱ Here,

• Radius = 14cm
• Pi = 22/7

● Substituting the values we get ,

${ : \implies} \rm \: Area_{(circle)} = \pi {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: Area_{(circle)} = \frac{22}{7} \times {(14)}^{2} \\ \\ \\ { : \implies} \rm \: Area_{(circle)} = \frac{22}{7} \times 196 \: \: \\ \\ \\ { : \implies} \rm \: Area_{(circle)} = \frac{4312}{7} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: Area_{(circle)} = { \pink{ \boxed{ \frak{616 {cm}^{2} }} \star}} \: \: \: \:$

• Henceforth the area of the circle is 616cm²

${ \large{ \underline{ \pmb{ \rm{ \circ \: Diagrams...}}}}}$

● Circle :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 14cm}\end{picture}$

● Square :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 20\ cm}\put(4.4,2){\bf\large 22\ cm}\end{picture}$

${ \large{ \underline{ \pmb{ \rm{ \circ \: More\: To\:know...}}}}}$

⠀⠀⠀⠀⠀

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Given:

• a wire in the form of square with side 22cm. it is reshaped and bent into the form of circle

To Find:

• calculate the area of this circle.

Solution:

We know that,

• Perimeter of a square = 4 times its side

Now,

• Side of the square is 22cm

Substituting,

➼ Perimeter = 22 × 4

➼ Perimeter = 88cm

As

• Perimeter of square equals perimeter of the circle

➼ Perimeter of the circle is 88cm

Now,

• Let's find the radius of the circle

Formula,

• Perimeter of the circle is 2πr

Substituting,

★ 88cm = 2πr

★ 88cm = 2 × 22/7 × r

★ Radius = 88×7/2×22

★ Radius = 14cm

Hence ,

• The radius of the circle is 14cm

Now,

• Let's find the area of the circle

Formula,

• Area of a circle is πr²

Substituting,

★ Area = 22/7 × 14 × 14

★ Area = 22×2×14

★ Area = 44 × 14

★ Area = 616cm²

Hence,

• The area of the circle is 616cm²