Question

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

Answer 1

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.

Complete step-by-step answer:

The circumference of the circle given is 616cm.
We know that the circumference of the circle is $2\pi r$.
So we can do $2\pi r$= 616cm
\[
  2 \times \dfrac{{22}}{7} \times r = 616{\text{cm}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {{\text{used}}\,\pi = \dfrac{{22}}{7}} \right] \\
  r = \dfrac{{616 \times 7}}{{44}} = 98{\text{cm}} \\
\]
Hence the radius is 98cm.
We know that the area of the quadrant off the circle whose radius is r can be written as:
$
   \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 $7546\,{\text{c}}{{\text{m}}^2}$.

Note: Whenever you face such types of problems you need to know that the only parameter we need in a circle is its radius to calculate the area, circumference etc. of any part of it. Proceeding in this way will solve your problem.