Question

Find the area of a circle whose circumference is 22cm.

Answer 1

Hint- In this question, we use the formula of circumference and area of circle. Circumference of the circle is \[2\pi r\] and area of the circle is $\pi {r^2}$ , where r is the radius of the circle. We can easily find the radius of a circle with the help of the formula of circumference of the circle.

Complete step-by-step solution -

Given, the circumference of the circle is 22cm.
Now, we apply the formula of circumference of the circle to find the radius of the circle.
So, circumference of circle $ = 2\pi r$
$ \Rightarrow 2\pi r = 22$
Put value of $\pi = \dfrac{{22}}{7}$
$ \Rightarrow 2 \times \dfrac{{22}}{7} \times r = 22$
Now, 22 cancel from both sides.
$
   \Rightarrow r = \dfrac{7}{2} \\
   \Rightarrow r = 3.5cm \\
 $
So, the radius of the circle is 3.5cm.
Now, we have to find the area of the circle so we apply the formula of area of circle in which radius of circle is 3.5cm.
Area of circle $ = \pi {r^2}$
$ \Rightarrow \pi \times {\left( {3.5} \right)^2}$
Put value of $\pi = \dfrac{{22}}{7}$
$
   \Rightarrow \dfrac{{22}}{7} \times {\left( {3.5} \right)^2} \\
   \Rightarrow \dfrac{{22}}{7} \times 3.5 \times 3.5 \\
   \Rightarrow 22 \times 0.5 \times 3.5 \\
   \Rightarrow 38.5c{m^2} \\
 $
So, the area of the circle is 38.5 $cm^2$.

Note-In such types of problems we can use two different ways to solve questions in an easy way. First way we already mentioned above and in the second way, we find the value of $\pi r$ and $r$ and put these values in the formula of the area of the circle.
$
   \Rightarrow 2\pi r = 22 \Rightarrow \pi r = 11 \\
   \Rightarrow r = \dfrac{{11}}{\pi } \\
  {\text{Area of circle}} = \pi {r^2} \\
   \Rightarrow \left( {\pi r} \right) \times r \\
   \Rightarrow 11 \times \dfrac{{11}}{\pi } \\
   \Rightarrow \dfrac{{121}}{{3.14}} \\
   \Rightarrow 38.5c{m^2} \\
 $