Question

If a wire is bent into the shape of a square, then the area of the square is $81c{m}^2$. When the same wire is bent into a semi-circular shape, then the area of the semi circle will be

• A. $22c{m}^2$
• B. $44c{m}^2$
• C. $77c{m}^2$
• D. $154c{m}^2$

Answer 1

The correct option is C $77c{m}^2$

Let the side of the square be $a$ cm

Thus, perimeter is $4a$ and area of the square is $a^2$

$\therefore a^2=81$

$\Rightarrow a=\sqrt{81}$

$\Rightarrow a=9$

Thus, perimeter $=4\times 9$ $=36$ cm

Now, wire is bent into a semicircle.

Therefore, $2r+\pi r=36$

$\Rightarrow r(\pi +2)=36$ $

$\Rightarrow r=\frac{36}{\frac{22}{7}+2}$

$\Rightarrow r=\frac{36}{\frac{36}{7}}$

$\Rightarrow r=7$ cm

Area of semicircle $=\frac{1}{2}\pi r^2$

$=\frac{1}{2}\times \frac{22}{7}\times 7\times 7$

$=77c{m}^2$