Question

If a wire is bent into the shape of a square, the area of the square is $81$ sq cm. When the wire is bent into a semicircular shape, what is the area of the semicircle? $(\pi =\frac{22}{7})$

• A. $77c{m}^2$
• B. $80c{m}^2$
• C. $75c{m}^2$
• D. $70c{m}^2$

Answer 1

Answer: (A)

$77c{m}^2$

Let $a$ be the length of each side of the square.

Then, $a^2=81\Rightarrow a=9cm$

$\therefore$ Length of wire $=$ Perimeter of square

$=4\times 9=36cm$

When the wire is bent into a semi-circular shape then, perimeter of semi circle $=\pi r+2r=36$

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

$=\frac{36\times 7}{(22+14)}$

$=\frac{36\times 7}{36}cm$

$=7cm$

Now,

Area of the semicircle $=\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 7\times 7c{m}^2$

$=77c{m}^2$