Question

Priyanka 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?

$\bigg( \sf\pi \: as \: \dfrac{22}{7} \bigg)$​

Answer 1

Answer:

Answer

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Given, Total length of the wire=44cm

∴ The circumference of the circle=2πr=44cm

⇒2×

7

22

×r=44

⇒r=

2×22

44×7

=7cm

Now, Area of the circle=πr

2

=

7

22

×7×7=154cm

2

Now the wire is converted into square,

Then perimeter of square=44cm

⇒4× side=44

⇒ side=

4

44

=11cm

Now, area of square=side×side=11×11=121cm

2

Therefore, on comparing the area of circle is greater than that of square, so the circle enclosed more area.

Answer 2

Step-by-step explanation:

⠀⠀

Given -

• Length of wire of circle is 44cm.

⠀⠀

To Find -

• Radius of Circle
• Area of Circle
• Perimeter of Square
• Area of Square
• Which encloses more area

⠀⠀

Formulae to be used -

• Circumference of Circle = $\sf2\pi r$
• Area of Circle = $\sf \pi {r}^{2}$
• Perimeter of Square = 4 × Side
• Area of Square = Side × Side

Where -

• R denotes radius
• S denotes sides
• $\pi$ denotes 22/7 ( ATQ )

Explanation -

The Question says that a girl priyanka took a wire whose Length is 44cm and bent or fence around the shape of circle. and we are ask to find the area of Circle, radius of circle after it . Ask to find perimeter of square and area of square.Also at last, we are ask to find that which encloses more area. So, let's do it -

⠀⠀⠀⠀

Now -

As we know that , According to given Question. Circumference of Circle is 44cm so, we have to find its Radius

⠀⠀

$\begin{gathered}\:\:\longrightarrow\sf{Circumference\;of\;Circle\;= 44cm}\\\\\longrightarrow \sf 2\pi r \:\:\:\:\:\: = \:\:\:44cm\\\\\longrightarrow \sf \: 2 \times \dfrac{22}{7} \times r \: = 44cm\\\\\longrightarrow \sf \: r \: = \: \cancel{44}^{2} \times \dfrac{1}{ \cancel{2}} \times \dfrac{7}{\cancel{22_1}}\\\\ \:\longrightarrow\sf \:r\: = 7cm\end{gathered}$

⠀⠀

$\therefore{\underline{\sf \: {Hence \: , \: Radius \: is \: \pmb{7cm}}}}$

⠀⠀

Now -

As per given Question, we have to find the area of Circle where radius is 7cm (approx).

⠀⠀

$\begin{gathered}\: \longrightarrow\sf{Area\;of\;circle\;=\;\pi {r}^{2} }\\\\\longrightarrow \sf \:Area_{\:(Circle)} = \dfrac{22}{7} \times 7 \times 7 \\\\\longrightarrow \sf \: Area_{\:(Circle)} = 154\:{cm}^{2} \end{gathered}$

⠀⠀

Now -

ATQ, we have to find the side of Square by using the formula of perimeter of Square and then we will apply the formula to find the area of Square.

⠀⠀

$\begin{gathered}\;\longrightarrow\sf{Perimeter\;of\;square\:=44cm}\\\\\longrightarrow\sf{4 \times side \: = \: 44cm }\\\\\longrightarrow \sf \: side \: = \cancel\dfrac{44}{4}\\\\\longrightarrow \sf side \: = 11cm\end{gathered}$

$\therefore{\underline{\sf \: {Hence \: , side \: of \: square \: is \: \pmb{11cm}}}}$

⠀⠀

$\begin{gathered}\:\longrightarrow\sf{Area\;of\;square\:=side \: \times \: side}\\\\\longrightarrow \sf \: 11 \times 11\\\\\longrightarrow \sf {Area \: = 121 \: cm}^{2} \end{gathered}$

⠀⠀⠀⠀

$\longrightarrow\sf \: Circle_{\:(Area)} = {154cm}^{2}\\\\\longrightarrow\sf \: Square_{\:(Area)} = {121cm}^{2}$

⠀⠀

$~~\large\green{\underline{\sf{Circle\;encloses\:more\:area\:than\:square}}}$

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