# Sketch the Region Bounded by Surfaces

I am presented with the following problem: Sketch the region bounded by the surfaces $z=\sqrt{x^2+y^2}$ and $x^2+y^2=1$ for $1$ less than/equal to $z$ greater than/equal to $2$.

I am not sure how to go about plotting this. I have tried multiple different ways but nothing seems to be working.

• You realize this is just the unit circle in the x-y plane translated by (0,0,1)? In any case note that RegionPlot3D requires a thickness to plot. If you'd like I can provide an answer where I show the shape using RegionPlot3D. – b3m2a1 Mar 9 '17 at 0:57
• Its fine, because the dawggie wants the bound area between those planes, not the planes themselves. – Tomi Mar 9 '17 at 1:03

## 1 Answer

Lets start with the first area (since we are considering the bound area, we can use equalities). Change the equality depending on a closed or open interval.

RegionPlot3D[Sqrt[x^2 + y^2] < z, {x, -4, 4}, {y, -4, 4}, {z, -4, 4}]


Bound it with the second

RegionPlot3D[
Sqrt[x^2 + y^2] < z && x^2 + y^2 < 1, {x, -4, 4}, {y, -4, 4}, {z, -4,
4}]


And then the final z condition

RegionPlot3D[
Sqrt[x^2 + y^2] < z && x^2 + y^2 < 1 && 1 <= z <= 2, {x, -4,
4}, {y, -4, 4}, {z, -4, 4}]


And there you have it.

• The two commands return a blank plot for me? EDIT: All the commands return a blank plot :( – naanman Mar 10 '17 at 4:16
• Can you post one command - also, what version of Mathematica :) – Tomi Mar 10 '17 at 10:47