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) 4

D) 12

Correct Answer: D

Solution :

\[{{x}^{2}}+{{y}^{2}}\le 16\]& \[\left| \,x\, \right|\ge y\]

(unshaded) Area\[=\frac{3}{4}\times \pi \times {{4}^{2}}=12\pi \]