Plot a set, given in cylindrical coordinates, with Maple and $\text{plot3d}$

Question

I want to plot the set $\phi(A)$ with Maple, where $$\phi:[0,\infty)\times[0,2\pi)\times\mathbb{R}\to\mathbb{R}^3\;,\;\;\;(r,\phi,z)\mapsto(r\cos\phi,r\sin\phi,z)$$ is the transformation in cylindrical coordinates and $$A:=[1,2]\times\left[0,\frac{\pi}3\right]\times[0,2]\;.$$ Unfortunatelly, the plot3d command expects an expression in two variables. How can I plot $\phi(A)$? It seems to be a simple task, but I wasn't able to figure out how to solve it.

Answer 1

Meanwhile, I figured it out. Actually, the solution is quite easy and natural:

common := coords = cylindrical: plots:-display([ plot3d([1, phi, z], phi = 0..Pi/3, z = 0..2, common), plot3d([2, phi, z], phi = 0..Pi/3, z = 0..2, common), plot3d([r, phi, 0], r = 1..2, phi = 0..Pi/3, common), plot3d([r, phi, 2], r = 1..2, phi = 0..Pi/3, common), plot3d([r, 0, z], r = 1..2, z = 0..2, common), plot3d([r, Pi/3, z], r = 1..2, z = 0..2, common) ], scaling = constrained, axes = boxed );