Step 1 Give the notes about how the triple integrals defined in cylindrical and spherical coordinates. Step 2 The cylindrical coordinates denotes a point P in space by ordered triples $(r,\theta ,z)\in t\hat{r}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\theta$ are polar coordinates for the vertical projection of P on the xy-plane with $r\ge \theta$ and z is the rectangular vertical coordinate. The equations related to the rectangular coordinates (x, y, z) and cylindrical coordinates $(r,\theta ,z)$ are, $x=r\mathrm{cos}\theta ,y=r\mathrm{sin}\theta ,z=z,{r}^{2}={x}^{2}+{y}^{2}$ and $\mathrm{tan}\theta =\frac{y}{x}$ Step 3 The spherical coordinates represent a point P in space by ordered triples $(p,\varphi ,\theta )$ in which, p is the distance from P to the origin $(p\ge 0)$ $\varphi$ is angle $over\to \left\{OP\right\}$ makes with the positive z-axis $(0\le \varphi \le \pi )$ $\theta$ is the angle from cylindrical coordinates. Step 4 The equations relating spherical coordinates to Cartesian and ctlindrical coordinates are, $r=p\mathrm{sin}\varphi$

$x=r\mathrm{cos}\theta =p\mathrm{sin}\varphi \mathrm{cos}\theta$

$z=p\mathrm{cos}\varphi$

$y=r\mathrm{sin}\theta =p\mathrm{sin}\varphi \mathrm{sin}\theta$

$p=\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}=\sqrt{{r}^{2}+{z}^{2}}$

$\mathrm{tan}\theta =\frac{y}{x}$ Cylindrical coordinates are good for describing cylinders whose axes run along the z-axis and planes that either contain the z-axis or lie perpendicular to the z-axis. Surfaces like these have equations of constant constant coordinate value.