Question

In the figure above, $O$ is the centre of the circle with diameter $10$. Find the length of minor arc $XY$, if the area of the shaded region is $\pi$

• A. $\frac{2\pi }{5}$
• B. $\frac{4\pi }{5}$
• C. $\frac{5\pi }{2}$
• D. $5\pi$

Answer 1

Answer: (A)

$\frac{2\pi }{5}$

Given diameter of circle is $10$ and area of the shaded region is $\pi$

Then radius of circle $=$ $\frac{10}{2}=5$

We know that area of circle whose radius is $r=$ $\pi r^2$

And circumference of circle is $2\pi r$

Then length of minor arc $XY=$ $\frac{2\pi r}{\pi r^2}\times \pi =\frac{2\pi }{r}=\frac{2\pi }{5}$