Question

A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm square. Find the length of the wire. If the same wire is bent to a larger circle, find:(i) radius of the circle formed.(ii) area of the circle.

Answer 1

Area of the square=484
Length of each side=side square=484
=22cm
Perimeter of the square=4*side
= 4*22
=88m
perimeter of the circle=88m
Radius=2πr=88
=2*22/7*r=88
=44/7r=88
r=14
area=πr square
=22/7*14
=44cm
Hope helped

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