Question

a wire when bent in a form of a square enclosed an area of 484 CM square if the same wire is bent in a form of a circle find the area enclosed by it

Answer 1

Here's the answer

Area of square = 484cm²

To find the side so that we can afterwards be able to find the length of wire


Area = side ²

$484 = {side}^{2}$

$side \: = \sqrt[]{484}$
side = 22

So,
the side is 22cm

Perimeter of square = 4 × SIDE

= 4 × 22

= 88cm

Here , 88cm will also be the circumference

To find radius

$circumference \: = 2\pi \: r$

let the radius be 'r'

$88 = 2 \times \frac{22}{7} \times r$

$\frac{88 \times 7}{2 \times 22} = r$

r = 14

so,
the radius is 14cm


to find the area

$area \: = \pi {r}^{2}$


$= \frac{22}{7} \times 14 \times 14$
= 616cm²


So,
the area enclosed is 616cm²

Answer 2

✰ ᴜɴᴅᴇʀsᴛᴀɴᴅɪɴɢ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ :

A metal wire is first bent into a square shape and had a area of 484 cm² .Next, the same wire is rebent into a circle shape. We have to find the radius and area of the circle and then we should find the length of the wire .

✰ɢɪᴠᴇɴ:

Area of the square = 484 cm²

✰ᴛᴏ ғɪɴᴅ:

length of the wire

radius of the circle

area of the circle

✰sᴏʟᴜᴛɪᴏɴ:

☛Length of the wire :

Let the side of the square be x

given that

➠Area of the square = 484 cm²

➠x² = 484 cm²

➠x = √484 cm²

➠$\boxed{\sf{x = 22 cm }}$

✰ɴᴏᴛᴇ:

As the same wire is bent into square and then into circle ,

length of the wire = Perimeter of the square = circumference of the circle

➠Perimeter of the square

➠4x

➠4(22)

➠88cm

therefore,

$\boxed{\sf{length of the wire = 88cm }}$

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☛Radius of the circle :

circumference of the circle = Perimeter of the square

➠2πr = 88

➠πr = 44

➠r = 44 × (7/22)

➠r = 2 × 7

➠r = 14 cm

$\boxed{\sf{Radius of the circle= 14 cm}}$

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☛Area of the circle:

➠area of the circle

➠πr² cm²

➠(22/7) × 14 × 14

➠44 × 14

➠616 cm²

$\boxed{\sf{area of the circle= 616cm² }}$

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✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:

SQUARE :

❏Perimeter= 4a units

❏Area = a² sq.units

❏Volume = a³ cu.units

CIRCLE :

❏Circumference = 2πr units

❏Area = π r² sq.units