question_answer

The area of the domain of the function           \[f(x,y)=\sqrt{16-{{x}^{2}}-{{y}^{2}}}-\sqrt{\left| x \right|-y}\] is \[k\pi \]Where k equals

A) 8                                             

B) 9

C) 10                                          

D) 12  

Correct Answer: D

Solution :

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 2nd radical sign \[y\le \,\,|x|\] i.e.,\[\frac{\text{3}}{\text{4}}\text{th}\] of the circle \[\therefore \]Required area \[=(\pi ,\,\,16)\frac{3}{4}=12\pi \]