Chapter 14.8, Problem 32E

(a)

To determine

To calculate: The volume of the solid which lies below the surface $f\left(x,y\right)=16-x^2-y^2$ and above the elliptical region $\frac{x^2}{16}+\frac{y^2}{9}\le 1$.

(b)

To determine

To calculate: The volume of the solid which lies below the surface $f\left(x,y\right)=A\cos \left(\frac{\pi }{2}\sqrt{\frac{x^2}{a^2}+\frac{y^2}{b^2}}\right)$ and above the elliptical region $\frac{x^2}{a^2}+\frac{y^2}{b^2}\le 1$.