Question

If $A$ and $B$ both lie on a circle and the length of $AB$ is $2\pi$, determine the radian measure of the central angle between $A$ and $B$, given that the area of the circle is $16\pi$ (In appropriate units)

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{2\pi }{3}$

Answer 1

The correct option is C $\frac{\pi }{2}$

Given area of circle is $16\pi$

And length of arc $AB=$ $2\pi$

We know area of circle $=$ $\pi R^2$

$\therefore \pi R^2=16\pi \Rightarrow R=4$

And we know that length of arc $=$ $\theta R$

$\therefore 2\pi =\theta \times 4$

$\Rightarrow \theta =\frac{2\pi }{4}$

$\Rightarrow \theta =\frac{\pi }{2}$