Question

Area of the region in which point $p(x,y),\{x>0\}$ , lies; such that $y\le \sqrt{16-x^2}$ and $\left|ta{n}^{-1}\left(\frac{y}{x}\right)\right|\le \frac{\pi }{3}$ is

• A. $\left(\frac{16}{3}\pi \right)$
• B. $(\frac{8\pi }{3}+8\sqrt{3})$
• C. $(4\sqrt{3}-\pi )$
• D. $(\sqrt{3}-\pi )$

Answer 1

The correct option is B $(\frac{8\pi }{3}+8\sqrt{3})$



Required area is the area of shaded region (APOQ)
= area of $\Delta OAQ$ + area of sector (OAP)
$=\frac{1}{2}\times 4\times 4\sqrt{3}+\frac{\pi (4\times 4)}{6}$
$=(\frac{8\pi }{3}+8\sqrt{3})$