Question

solve the following problem

Answer 1

Given :-

• A wire which resembles as a square of side 22cm is rebent in the form of circle.

______________________

To find :-

• Radius of circle formed

• Which figure will have more area

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Solution :-

Since length of wire remains same in both figures: square and circle, so we can take their perimeter as equal. We will solve the question on this concept and also use concept of area.

So let's began by finding radius of circle!

⇒ Perimeter of circle=Perimeter of square

$\maltese$ Now here, applying formula:

• Perimeter of circle=2πr

• Perimeter of square=4×Side

⇒ 2πr=4×Side

Substituting value of side of square

⇒ 2πr=4×22

Now transporting variable (radius) and numerical values on different sides.

$\sf \implies r=\dfrac{4\times 22}{2\pi }$

Substituting value of π

$\sf \implies r=\dfrac{4\times 22}{2\times\cfrac{22}{7} }$

$\sf \implies r=\dfrac{4\times 22\times 7}{2\times 22 }$

By solving it we get:

$\large\boxed{\sf \implies r=14cm}$

So the required value of radius is 14cm.

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• Now finding which figure encloses more area:

~For square

Area of square=Side²

Area of square=(22cm)²

Area of square=484cm²

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~For circle

Area of circle=πr²

Area of circle=22/7×(14cm)²

Area of circle=22/7×196cm²

Area of circle=22×28cm²

Area of circle=616cm²

So the given wire will enclosed more area in the form of circle.

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Answer 2

ɢɪᴠᴇɴ :-

• side of square = 22 cm
• perimeter of square = perimeter of circle

ᴛᴏ ғɪɴᴅ :-

• radius of circle = ?
• which shape encloses more area ?

sᴏʟᴜᴛɪᴏɴ :-

• perimeter of square = 4 × side
• = 4 × 22 cm = 88 cm

• perimeter of circle = perimeter of square
• 2 π r = 88 cm
• $\sf{2 \times \frac{22}{7} \times r = 88cm }$
• $\sf{ \frac{44 \: r}{7} = 88 cm}$
• $\sf{r = \frac{88 \times7}{44} }cm$
• $\boxed{ \sf{r = 14cm}}$

Now,

• Area of square = side × side
• = 22 × 22 cm²
• = 484 cm²

And,

• Area of circle = π r²
• =
• $\sf{ \frac{22}{7} \times (14) {}^{2} \: cm {}^{2} }$
• $\sf{= \frac{22}{7} \times 14 \times 14 \: cm {}^{2} }$
• $\sf{ = 616 \: cm {}^{2} }$

So,

• radius of circle = 14 cm
• circle encloses more area than square