$AC$ and $BD$ are two perpendicular diameters of a circle $ABCD$. Given that the area of the shaded portion is $308c{m}^2$, calculate the circumference of the circle.

The correct option is F. $88cm$

Given:

$AC$ and $BD$ are two perpendicular diameters of a circle $ABCD$.

i.e., in figure, circle divides into four quadrants.

So, $2\times$ area of the shaded region $=$ Area of circle

$\Rightarrow \pi r^2=308c{m}^2$

$\Rightarrow \frac{22}{7}{r}^2=2\times 308c{m}^2$

$\Rightarrow r^2=2\times \frac{7}{22}\times 308c{m}^2$

$\Rightarrow r^2=2\times 7\times 14c{m}^2$

$\Rightarrow r^2=(14cm{)}^2$

$\Rightarrow r=14cm$

Now, the circumference of a circle $=2\pi r$

$=2\times \frac{22}{7}\times 14cm$

$=88cm$