Question

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

Answer 1

When wire is in the form of rectangle-

Length of rectangle $\left(l\right)=40cm$

Breadth of rectangle $\left(b\right)=26cm$

Perimeter of rectangle $=2(l+b)$

$\Rightarrow$ Perimeter of rectangle $=2(40+26)=132cm$

Area enclosed by the rectangle $\left(A_1\right)=l\times b$

$\Rightarrow A_1=40\times 26=1040{cm}^2$

When the wire is in the form of circle-

Perimeter of circle will be equal to perimeter of rectangle.

$\therefore$ Perimeter of circle $=132cm$

$\Rightarrow 2\pi r=132$

$\Rightarrow r=\frac{132}{2}\times \frac{7}{22}=21cm$

Thus the radius of circle is $421cm$

Now,

Area enclosed by the circle $\left(A_2\right)=\pi r^2$

$\Rightarrow A_2=\frac{22}{7}\times {\left(21\right)}^2=1386{cm}^2$

$\because A_2>A_1$

$\therefore A_2-A_1=1386-1040=346{cm}^2$

Hence the circle encloses more area than rectangle by $346{cm}^2$.