Let D be the region bounded below by the plane zequals=​0, above by the sphere x squared plus y squared plus z squared equals 900x2+y2+z2=900​, and on the sides by the cylinder x squared plus y squared equals 100x2+y2=100. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration. a. dz dr dthetaθ b. dr dz dthetaθ c. dthetaθ dz dr

Answer:The cylinder is given straight away by x^2+y^2=r^2=16\implies r=4. To get the cylinder, we complete one revolution, so that 0\le\theta\le2\pi. The upper limit in z is a spherical cap determined byx^2+y^2+z^2=144\iff z^2=144-r^2\implies z=\sqrt{144-r^2}So the volume is given by\displaystyle\iiint_{\mathcal D}\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}\int_{z=0}^{z=\sqrt{144-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\thetaand has a value of \dfrac{128(27-16\sqrt2)\pi}3 (not that we care)Read more on Brainly.com - explanation: