Question

$\: ~~~~~{\underline{\frak{\orange{~Question~}}}}$

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 square,what will be the length of each of its sides? Which figure encloses more area, the circle or the square? Take ( $\pi$ = $\sf \dfrac{22}{7}$ )

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Answer 1

Given:-

• Length of Wire = 44cm

To Find:-

• Radius of the Circle
• Area of the Circle
• Perimeter of the Square
• Area of the Square
• Which encloses more area ( ○ or □ )

Using Formulas:-

• Circumference of Circle = ${2 \pi r}$
• Area of Circle = ${ \pi r²}$
• Perimeter of Square = 4 × Side
• Area of Square = Side × Side

Solution with step by Step Explanation:-

Here's Questions Say that take $\pi$ as $\sf\dfrac{22}{7}$ So,

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Circumference of Circle = 44

$\begin{gathered}\sf:\implies{ 2 \pi r = 44cm}\\\\\\ :\implies\sf{2 \times \sf\dfrac{22}{7} \times r = 44 }\\\\\\ :\implies\sf{r = {\cancel {44}^{2}} \times \dfrac{1}{\cancel{2}} \times \dfrac{7}{\cancel{22_1}} = 7cm } \\ \\ \: {\underline{\sf{\orange{~Now, we ~have~to~find~the~area~of~Circle}}}}\\\\\\:\implies\sf{Area~of~Circle = \pi r²}\\\\\\:\implies\sf{ \dfrac{22}{\cancel{7}}\times {\cancel{7}}\times 7= 154cm²}\\\\\\ \end{gathered}$

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$\begin{gathered}{\underline{\sf{\orange{Now, Lets~find~perimeter ~of ~Square}}}}\\\\\\:\implies\sf{Perimeter ~of~Square = 44} \\ \\ :\implies \sf{4\times Side = 44}\\\\:\implies \sf{Side = \dfrac{44}{4} = 11cm}\\\\ \dag\: {\underline{\sf{\pink{Now~let's ~find~the ~area~of~circle}}}}\\\\\\ :\implies \sf{Area~of~Square = Side \times Side }\\\\:\implies\sf{11 \times 11 }\\\\:\implies\sf{121cm²}\\\\\\\\\end{gathered}$

${\underline {\frak{~~~154cm² > 121 cm²}}}$

$\therefore {\underline{\rm{\green{Circle~ encloses ~more~ Area ~ than~ square }}}}$

Answer 2

Given -

• Length of wire = 44 cm

To find -

• Radius of circle and it's area and also the length of square.

Formulae used -

• Circumference of circle

• Area of circle

• Perimeter of square

• Area of square

Solution -

In the question, we are provided with the length of wire, and we need to find the radius + area of a circle and also if the same wire is bent into square, then we have to find it's length. So first, we will take radius as r, then we will apply the formula of circumference of circle to find the radius, after that we will apply the formula of area of circle to find the area of the circle. After that we will find the length of each side of the square, by applying the formula of perimeter of square.

According to question -

Length of wire = 44cm

Circumference of circle -

2πr = 44cm

π = $\sf\dfrac{22}{7}$

r = Radius

On substituting the values -

$\sf \longrightarrow\: 2\pi \: r = c\\ \\ \sf \longrightarrow \: r \: = \frac{44cm}{2\pi} \\ \\ \sf \longrightarrow \: r \: = \frac{44 \: \times 7}{2 \: \times 22} \\ \\ \sf \longrightarrow \: r \: = 7cm$

Now -

We will find the length of each side of the square, by applying the formula of perimeter of square. In this case, the perimeter of the square will be equal of 44cm.

$\sf \longrightarrow \: p = 4 \: \times side \\ \\ \sf \longrightarrow \: 44cm \: = 4 \times \: side \\ \\ \sf \longrightarrow \: side \: = \frac{44}{4} \\ \\ \sf \longrightarrow \: side \: = 11cm$

Now -

We will find the area of square, by applying the formula of area of square.

$\sf \longrightarrow \: a = {(side)}^{2} \\ \\ \sf \longrightarrow \: a \: = {(11cm)}^{2} \\ \\ \sf \longrightarrow \: a \: = 121 {cm}^{2}$

Similarly -.

We will find the area of the circle, by applying the formula of area of circle.

$\sf \longrightarrow \: a \: = \pi {r}^{2} \\ \\ \sf \longrightarrow \: a \: = \dfrac{22}{7} \: \times \: {(7cm)}^{2} \\ \\ \sf \longrightarrow \: a \: = \dfrac{22}{7} \: \times \: 49cm \\ \\ \sf \longrightarrow \: a \: = 22 \: \times 7 \\ \\ \sf \longrightarrow \: a \: = 154cm^{2}$

So -

$\sf \longrightarrow \: 154cm > 121cm$

$\therefore$ Circle's area is greater than square's area.