Question

Find the area of the quadrant of a circle whose circumference is 44 cm.

Answer 1

Hint: In circles, if we have a circle of radius r then the circumference of this circle is given by the formula 2$\pi $r and the area of this circle is given by the formula $\pi {{r}^{2}}$.Here,quadrant means $\dfrac{1}{4}$ of circle.Using this, we can solve this question.

“Complete step-by-step answer:”
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
Let us consider a circle of radius r. The circumference of this circle is given by the formula,
$C=2\pi r$ . . . . . . . . . . . . (1)
The area of the circle is given by the formula,
$A=\pi {{r}^{2}}$ . . . . . . . . . . . . . . . (2)
In this question, we are given a circle having its circumference = 44 cm. Let us assume r be the radius of this circle. Substituting C = 44 in formula (1), we get,
$44=2\pi r$
$\Rightarrow r=\dfrac{22}{\pi }$
Substituting this value of r in the formula (2), we get the area of this circle equal to,
$\begin{align}
  & A=\pi {{\left( \dfrac{22}{\pi } \right)}^{2}} \\
 & \Rightarrow A=\dfrac{{{22}^{2}}}{\pi } \\
\end{align}$
Substituting $\pi =\dfrac{22}{7}$, we get,
$\begin{align}
  & A=\dfrac{{{22}^{2}}}{\dfrac{22}{7}} \\
 & \Rightarrow A=22\times 7 \\
 & \Rightarrow A=154c{{m}^{2}} \\
\end{align}$
Since we are required to find the area of the quadrant of this circle, we have to divide the above area by 4. So, the area of the quadrant of this circle is equal to $\dfrac{1}{4}\left( 154 \right)=38.5c{{m}^{2}}$.
Hence, the answer is $38.5c{{m}^{2}}$.

Note: There is a possibility that one may write the area of the whole circle instead of the area of the quadrant of this circle as the answer. So, in order to avoid such types of mistakes, one must read the question carefully.