Question

$AC$ and $BD$ are two perpendicular diameters of a circle $ABCD$. It is given that the area of the shaded portion is $308c{m}^2$. Then the length of $AC$ is

• A. $28$ cm
• B. $14$ cm
• C. $7$ cm
• D. $10$ cm

Answer 1

The correct option is A $28$ cm

Given- In the given figure $AC$ and $BD$ are two diameters of a circle with centres as $O$.

$AC\perp BD$

Area $ADCOA=308m^2$

To find out- $AC=?$

Solution-

$AC$ is a diameter of the given circle.

$\therefore ADCOA$ is a semicircle.

Let $AC=2r$

Then $OC=\frac{1}{2}\times AC=\frac{1}{2}\times 2r=r=$ radius of the semicircle.

So, area semicircle $=A=\frac{1}{2}\pi r^2=308$ .....(given)

$\Rightarrow r^2=\frac{2\times 308}{\pi }=\frac{2\times 308}{\frac{22}{7}}{m}^2=196m^2$

$\Rightarrow r=\sqrt{196}$ m $=14$ m

$\therefore AC=2r=2\times 14$ m $=28$ m