# Identifying the surface $z=(9-x^2-y^2)^{1/2}$

I have to identify the equation $z = (9-x^2-y^2)^{1/2}$.

When I use traces to plot it, it looks like an upside down net trap. I'm not exactly sure if that kind of surface has a name. Does it?

What's all them more confusing is that I expected it to be the top half of a sphere because if you simplify the formula given it looks like $z^2+x^2+y^2=9$.

• It is the top half of a sphere, for exactly the reason you gave. Perhaps something went wrong with your plot. Can't make any further suggestions because I don't know what a net trap looks like :) Dec 4, 2017 at 1:42

I don't know what a "net trap" is supposed to look like, but what might be confusing you is that typical computer plotting tools might produce something like this:

Basically the problem is that your function only has real values for $(x,y)$ in a disk, but the plotting software is evaluating the function at points of a rectangular grid. The software leaves out cells of the grid containing a point outside this disk, causing a jagged-looking edge of the image.

• Oh! Yeah, that makes a lot of sense :) I was using winplot and it had jagged edges too Dec 4, 2017 at 2:04

It is the surface of a hemisphere with radius $3$ and centered at the origin.

In future you can use the link provided below

https://www.desmos.com/calculator/ongcgqgcpr

$f(x,y)=\sqrt{9-x^2-y^2}$