Question

# Find the area of a quadrant of a circle whose circumference is 616cm.

Hint: In order to solve this problem first find the radius with the help of circumference of the circle. Then find the area by using the formula $\dfrac{{\pi {r^2}}}{4}$. Doing this will solve your problem.

We know that the circumference of the circle is $2\pi r$.
So we can do $2\pi r$= 616cm
$2 \times \dfrac{{22}}{7} \times r = 616{\text{cm}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {{\text{used}}\,\pi = \dfrac{{22}}{7}} \right] \\ r = \dfrac{{616 \times 7}}{{44}} = 98{\text{cm}} \\$
$\Rightarrow \dfrac{{\pi {r^2}}}{4} \\ \Rightarrow \dfrac{{22 \times {{(98)}^2}}}{{7 \times 4}} = 7546\,{\text{c}}{{\text{m}}^2} \\$
Hence the area of the quadrant is $7546\,{\text{c}}{{\text{m}}^2}$.