Question

A piece of wire is in the form of a rectangle whose length and breadth are 40 cm and 26 cm
respectively. It is bent in the form of a circle. Find the radius of the cirle. Also find the area of the
circle and the rectangle. Which figure encloses more area and by how much?​

Answer 1

Given : A piece of wire is in the form of rectangle whose length and breadth are 40 cm and 26 cm respectively it is bent in the form of a circle. To find : The radius of the circle? Therefore, The radius of the circle is 21 cm.

full explanation .

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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 × 227

=21cm

Thus the radius of circle is $421 \; cm$$

Now,

Area enclosed by the circle (A 2 )=πr 2

⇒A 2 = 722

×(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

$When wire is in the form of rectangle-</p><p></p><p>Length of rectangle (l)=40cm</p><p></p><p>Breadth of rectangle (b)=26cm</p><p></p><p>Perimeter of rectangle =2(l+b)</p><p></p><p>⇒ Perimeter of rectangle =2(40+26)=132cm</p><p></p><p>Area enclosed by the rectangle (A1)=l×b</p><p></p><p>⇒A1=40×26=1040cm2</p><p></p><p>When the wire is in the form of circle-</p><p></p><p>Perimeter of circle will be equal to perimeter of rectangle.</p><p></p><p>∴ Perimeter of circle =132 cm</p><p></p><p>⇒2πr=132</p><p></p><p>⇒r=2132×227=21cm</p><p></p><p>Thus the radius of circle is 421 \; cm </p><p></p><p>Now,</p><p></p><p>Area enclosed by the circle (A2)=πr2</p><p></p><p>⇒A2=722×(21)2=1386cm2</p><p></p><p>∵A2>A1</p><p></p><p>∴A2−A1=1386−1040=346cm2</p><p></p><p>Hence the circle encloses more area than rectangle by 346cm2.</p><p></p><p>$

∴A2−A1=1386−1040=346cm2

Hence the circle encloses more area than rectangle by 346cm2.

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