A piece of wire is in the form of a rectangle whose length is 52 cm and breadth is 36 cm. It is cut at a point and bent in the form of a circle . find the radius of a circle
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Step-by-step explanation:
When wire is in the form of rectangle-
Length of rectangle (l)=40cm
Breadth of rectangle (b)=26cm
Perimeter of rectangle =2(l+b)
⇒ Perimeter of rectangle =2(40+26)=132cm
Area enclosed by the rectangle (A
1
)=l×b
⇒A
1
=40×26=1040cm
2
When the wire is in the form of circle-
Perimeter of circle will be equal to perimeter of rectangle.
∴ Perimeter of circle =132 cm
⇒2πr=132
⇒r=
2
132
×
22
7
=21cm
Thus the radius of circle is $421 \; cm$$
Now,
Area enclosed by the circle (A
2
)=πr
2
⇒A
2
=
7
22
×(21)
2
=1386cm
2
∵A
2
>A
1
∴A
2
−A
1
=1386−1040=346cm
2
Hence the circle encloses more area than rectangle by 346cm
2
.
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