Question

A metal wire, when bent in the form of an

equilateral triangle of largest area, encloses an

an

area of 484 V3 cm2. If the same wire is bent

into the form of a circle of largest area, find

the area of this circl​

Answer 1

Answer:

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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,

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

━━━━━━━━━━━━━━━━━━━━━━

☛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

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

━━━━━━━━━━━━━━━━━━━━━━

☛Area of the circle:

➠area of the circle

➠πr² cm²

➠(22/7) × 14 × 14

➠44 × 14

➠616 cm²

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

━━━━━━━━━━━━━━━━━━━━━━

✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:

SQUARE :

❏Perimeter= 4a units

❏Area = a² sq.units

❏Volume = a³ cu.units

CIRCLE :

❏Circumference = 2πr units

❏Area = π r² sq.units

Answer 3

✰ 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,

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

━━━━━━━━━━━━━━━━━━━━━━

☛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

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

━━━━━━━━━━━━━━━━━━━━━━

☛Area of the circle:

➠area of the circle

➠πr² cm²

➠(22/7) × 14 × 14

➠44 × 14

➠616 cm²

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

━━━━━━━━━━━━━━━━━━━━━━

✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:

SQUARE :

❏Perimeter= 4a units

❏Area = a² sq.units

❏Volume = a³ cu.units

CIRCLE :

❏Circumference = 2πr units

❏Area = π r² sq.units

Answer 4

✰ 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,

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

━━━━━━━━━━━━━━━━━━━━━━

☛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

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

━━━━━━━━━━━━━━━━━━━━━━

☛Area of the circle:

➠area of the circle

➠πr² cm²

➠(22/7) × 14 × 14

➠44 × 14

➠616 cm²

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

━━━━━━━━━━━━━━━━━━━━━━

✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:

SQUARE :

❏Perimeter= 4a units

❏Area = a² sq.units

❏Volume = a³ cu.units

CIRCLE :

❏Circumference = 2πr units

❏Area = π r² sq.units

Answer 5

✰ 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,

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

━━━━━━━━━━━━━━━━━━━━━━

☛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

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

━━━━━━━━━━━━━━━━━━━━━━

☛Area of the circle:

➠area of the circle

➠πr² cm²

➠(22/7) × 14 × 14

➠44 × 14

➠616 cm²

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

━━━━━━━━━━━━━━━━━━━━━━

✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:

SQUARE :

❏Perimeter= 4a units

❏Area = a² sq.units

❏Volume = a³ cu.units

CIRCLE :

❏Circumference = 2πr units

❏Area = π r² sq.units