(Solved): 10. Let D be the region bounded below by the cone z=x2+y2 and above by the sphere z=64x2y2 ...

10. Let $\mathrm{D}$ be the region bounded below by the cone $z=\sqrt{x^2+y^2}$ and above by the sphere $z=\sqrt{64-x^2-y^2}$ set up the triple integral in cylindrical coordinate that gives the volume of $\mathrm{D}$ using the order of integration dzdrd $\theta$. 11. Set up the iterate integral for evaluating ${\iiint }_{D}f(r,\theta ,z)dzrdrd\theta$ over the region D (a) $\mathrm{D}$ is the right circular cylinder whose base is the circle $r=2\sin \theta$ in the $xy$-plane and whose top lies in the plane $z=9-y$. (b) $\mathrm{D}$ is the rectangular solid whose base is the triangle with vertices at $(0,0),(0,8)$, and $(8,8)$ and whose top lies in the plane $z=5$. 12. Use the spherical coordinate integral to find the volume of the given solid. (a) The solid bounded below by the sphere $\rho =6\cos \varphi$ (b) the solid enclosed by the cardioid of and above by the cone $z=\sqrt{x^2+y^2}$. revolution $\rho =5+3\cos \varphi$. 13. Let $\mathrm{D}$ be the region that is bounded below by the cone $\varphi =\frac{\pi }{4}$ and above by the sphere $\rho =4$. Set up the triple integral for the volume $\mathrm{D}$ in cylindrical coordinate.