Show your steps to justify your answer. Write your solution properly, neatly, and carefully.

Let $E$ be the solid upper half cone of radius $R$ and height $h,$ which lies above the conical surface $z=\frac{h}{R}\sqrt[\phantom{2}]{x^2+y^2}$ and below the horizontal plane $z=h,$ as shown above.

Suppose that $E$ has constant density $.$ Then the mass of $E$ is $m={}_{E}dV,$ and the moments of $E$ about the coordinate planes are given by:

$M_{yz}={}_{E}xdV,M_{xz}={}_{E}ydV,M_{xy}={}_{E}zdV$

The center of mass of $E$ is located at the point $C=(\stackrel{}{x}\frac{,}{b}ar(y)\frac{,}{b}ar(z)),$ where $\stackrel{}{x}=\frac{M_{yz}}{m}\frac{,}{b}ar(y)=\frac{M_{xz}}{m}\frac{,}{b}ar(z)=\frac{M_{xy}}{m}.$ Find the center of mass of $E.$

$($Hints: Use cylindrical coordinates. You may use the fact that ${\displaystyle \underset{0}{\overset{2}{}}}cosd=0={\displaystyle \underset{0}{\overset{2}{}}}sind.)$