Question

If a wire is bent into the shape of a square, then the area of the square is $81sq.cm.$ When the wire is bent into a semi-circular shape, 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

Answer: (C)

$77c{m}^2$

Given wire is bent in form of square

Let the square side be $acm$

Area of square $=a^2=81sq.cm$ (Given)

$\Rightarrow a=\sqrt{81}=9cm$

As wire is bent into a square , perimeter of square equals length of wire.

Perimeter of square $=4\ast side=4a=36cm$.

$\Rightarrow$Length of wire $=36cm$

Now wire is bent into a semicircle.

Let the radius of semi-circle be $rcm$.

Perimeter of semi-circle$=(2+\pi )r$

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

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

Area of semi-circle $=\frac{1}{2}\pi r^2$

$=\frac{\pi \ast 7^2}{2}=76.93c{m}^2$