Question

$\large{\sf{\underline{\underline\pink{Question!!}}}}$

Shazil took a wire of length 44cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square?

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Answer 1

Answer:

$\frak{Given}\begin{cases}\sf{Length\:of\:the\:wire=\bf 44\:cm.}\\\sf{First,it\:is\:bent\:to\:form\:a\:\bf Circle. }\\\sf{Then,it\:is\:re-bent\:to\:form\:a\:\bf Square. }\end{cases}$

$\underline{\bf\bigstar\:To\:Find:-}$

• Radius of the circle formed.
• Area of the circle.
• Length of each side of the square formed.
• The figure (square/circle) which encloses more area

$\underbrace{\underline{\bf\bigstar\:Solution:-}}$

» Since the same wire is used throughout so, the perimeter of every figure formed would be equal to the length of the wire.

◆ Finding the Radius and the Area of the Circle :

» The length of the wire would be equal to the circumference of the circle.

So,

$\colon \rarr \sf \: length _{ \: wire} = circumference_ { \: circle} \\ \\ \colon \rarr \bf \: \cancel{44 }\: {cm }= \bf \cancel 2\pi r \\ \\ \displaystyle\colon \rarr \bf \: \cancel{22} \: cm = \dfrac{ \cancel{22}}{7} \times r \\ \\ \colon \dashrightarrow \boxed{\boxed{\pink{ \frak{ r = 7 \: cm}}}}$

And,

$\colon \rarr \sf \: area _{ \: circle} = \pi {r}^{2} \\ \\ \colon \bf \rarr \: area _{ \: circle}= \frac{22}{ \cancel7} \times \cancel 7 \times 7 \: {cm}^{2} \\ \\ \colon \rarr \bf \: area _{ \: circle} = 22 \times 7 \: {cm}^{2} \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \purple{ \frak{area _{ \: circle} = 154 \: {cm}^{2} }}}}$

◆ Finding the side and the area of the square :

» The length of the wire would be equal to the perimeter of the square.

So,

$\colon \rarr \sf \: length _{ \: wire} = perimeter _{ \: square} \\ \\ \colon \rarr \bf \: \cancel{44 }\: cm = \cancel4 \times side \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \frak{ \pink{side = 11 \: cm}}}}$

And,

$\colon \sf \rarr \: area _{ \: square} = {side}^{2} \\ \\ \colon \rarr \bf \: area _{ \: square} = {(11 \: cm)}^{2} \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \frak{ \pink{area _{ \: square} = 121 \: {cm}^{2} }}}}$

◆ Figure which encloses more area :

» We know

• Area of Circle = 154 cm²
• Area of Square = 121 cm²

» The value of Area of Circle is greater than the value of the Area of Square .

$\therefore\;\underline{\bf \red{Circle}\:\sf{encloses\:more\:area.}}$

_____________________________

Answer 2

$\huge\blue{\boxed{\blue{ \bold{\fcolorbox{red}{black}{\green{QUESTION}}}}}}$

Shazli took a wire of length 44cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take π= 22/7 ).

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

• (Refer to attachment)

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