Question

The perimeter of the square and circumference of the circle are equal, the area of the square is $121{m^2}$ then find the area of the circle.

Answer 1

Hint- In order to solve these types of questions first write what is given to us. This will give us a clear picture of what our approach should be then apply the required answer. Here we have to use the formula for the area of circle i.e. $\pi {r^2}$.

Complete step-by-step answer:

Now, we have given that the perimeter of the square and the circumference of the circle are equal.
And we have to find the area of the circle.
Also we have given that area of square $ = 121{m^2}$
Now, we know that
Perimeter of square =$4s$
And circumference of circle = $2\pi r$
Given that, the perimeter of square and circumference of circle are equal
$ \Rightarrow 4s = 2\pi r$
$\Rightarrow 4 \times s = 2 \times \dfrac{{22}}{7} \times r$
$\Rightarrow r = \dfrac{{s \times 4 \times 7}}{{22 \times 2}}$
$\Rightarrow r = \dfrac{{7s}}{{11}}$ --------(1)
Now area of square =121
We know that area of square =${s^2}$
$ \Rightarrow {s^2} = 121$
$s = \sqrt {121} $
$\Rightarrow s = 11$ m
Now put the value of $s$ in (1) we get,
$r = \dfrac{{7 \times 11}}{{11}}$
$\Rightarrow r = 7m$
Now the area of circle =$\pi {r^2}$
=$\dfrac{{22}}{7} \times {\left( 7 \right)^2}$
Or area of circle = $22 \times 7$
=$154{m^2}$
Thus the area of circle = $154{m^2}$

Note- Whenever we face such types of questions the key concept is that we should write what is given to us then apply the required formula like we did in this question. Here, we simply find the value of s i.e. the side of a square then we find the value of radius of circle and then we find the area of circle . Thus we get our required answer.