Question

What is the area of a circle whose circumference is same as the perimeter of square of side 44 cm?

• A. 2000 $c{m}^2$
• B. 2364 $c{m}^2$
• C. 2464 $c{m}^2$
• D. 2564 $c{m}^2$

Answer 1

The correct option is C 2464 $c{m}^2$

We know that the perimeter of a square = 4 x side
So, the perimeter of the given square = 4 x 44 cm = 176 cm
Also, we know, circumference of a circle = 2 $\pi$ r
The circumference of the circle and perimeter of the square are equal.
$\Rightarrow$ 176 = 2 $\pi$ r
$\Rightarrow$ 176 = 2 x$\frac{22}{7}$ x r
$\Rightarrow$ r = 28 cm
Also, the area of a circle = $\pi$ $r^2$
= $\frac{22}{7}$ x ${28}^2$
= 2464 $c{m}^2$