Please help, I tried $to$ run the code but errors popped $up$ and I cannot move past. Please advise how I $am$ able $to$ fix this. I have attached all parts $of$ #$1$ here $in$ photos. Thanks $in$ advance

Problem $1$: Consider the iterated integral $in$ cylindrical coordinates ${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}{\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{r^3}{\overset{r}{}}}rdzdrd.$

$a\%$ Convert cylindrical coordinates $to$ Cartesian coordinates

$x=r.*cos(theta)$;

$y=r.*sin(theta)$;

$\%$ Apply the mask $to$ get the valid points

$x_v$alid $=x(mask)$;

$y_v$alid $=y(mask)$;

$z_v$alid $=z(mask)$;

$\%$ Plot the solid region using trisurf

trisurf$(delaunay(x_v$alid, $y_v$alid$),x_v$alid, $y_v$alid, $z_v$alid, 'Facecolor', 'cyan', 'EdgeColor', 'none'$)$;

Warning: Duplicate data points have been detected and removed.

Some point indices will not $be$ referenced $by$ the triangulation.

$\%$ Set the view and Labels for better visualization

view$(3)$;

xlabel$(\text{'}x\text{'})$;

ylabel$(\text{'}y\text{'})$;

zlabel$(\text{'}z\text{'})$;

title$(\text{'}Solid$ Region $in$ Cylindrical Coordinates'$)$;

axis equal;

grid $on$; $bVof$ the solid.

Solution: The value $of$ the integral, representing the volume $Vof$ the solid, $isP\frac{i}{9.}$

The given iterated integral $is$:

${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}{\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{0}{\overset{r}{}}}rdzdrd$

The integral $is$ solved step$-by-$step:

Integrate with respect $toz$ :

${\displaystyle \underset{0}{\overset{r}{}}}rdz=rz{|}_0^r=r(r)-r(0)=r^2$

Integrate with respect $tor$ :

${\displaystyle \underset{0}{\overset{1}{}}}{r}^{2}dr=\frac{r^3}{3}{|}_0^1=\frac{1^3}{3}-\frac{0^3}{3}=\frac{1}{3}$ Integrate with respect $to$ :

${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}\frac{1}{3}d=\frac{1}{3}{|}_0^{\frac{}{3}}=\frac{1}{3}(\frac{}{3})-\frac{1}{3}(0)=\frac{}{9}$

$c$