Question

The area of the domain of the function $f(x,y)=\sqrt{16-x^2-y^2}-\sqrt{|x|-y}$ is $k\pi$ where $k$ equals

• A. 8
• B. 9
• C. 10
• D. 12

Answer 1

Answer: (D)

From the first radical sign
$x^2+y^2\le 16$ i.e. interior of a circle with circle $(0,0)$ and radius 4 .
From the $2^{\text{nd }}$ radical sign $y\le |x|$
i.e. $\frac{3}{4}$ th of the circle
$\therefore$ Required area $=(\pi \cdot 16)\frac{3}{4}=12\pi$.