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
Answers
Area of square = 484cm²
To find the side so that we can afterwards be able to find the length of wire
Area = side ²
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
let the radius be 'r'
r = 14
so,
the radius is 14cm
to find the area
= 616cm²
So,
the area enclosed is 616cm²
✰ 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
➠
✰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,
━━━━━━━━━━━━━━━━━━━━━━
☛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
━━━━━━━━━━━━━━━━━━━━━━
☛Area of the circle:
➠area of the circle
➠πr² cm²
➠(22/7) × 14 × 14
➠44 × 14
➠616 cm²
━━━━━━━━━━━━━━━━━━━━━━
✰ʀᴇʟᴀᴛᴇᴅ ғᴏʀᴍᴜʟᴀ:
SQUARE :
❏Perimeter= 4a units
❏Area = a² sq.units
❏Volume = a³ cu.units
CIRCLE :
❏Circumference = 2πr units
❏Area = π r² sq.units