I have the following problem:
A part, $\Omega$ of a filled sphere is given by:
$$\Omega=\{(x,y,z)\in \mathbb{R}^3 | \: x^2+y^2+z^2 ≤1, x≥0, -x ≤y ≤x, z ≥0 \}$$
Determine a parametric equation for $\Omega$.
Okay, so my first instinct was to look at the general equation for a filled sphere and then change the intervals so that it matched the requirements.
$$(x,y,z)=\bigg(\sin(\theta)\cos(\phi), \: \sin(\theta)\sin(\phi),\: \cos(\theta) \bigg),\theta\in[0,\pi], \:\phi\in[0,2\pi]$$
But when I change the intervals, for example instead of $\theta\in[0,\pi]$ I do $\theta\in[0,\frac{\pi}{2}]$ it no longer has the sphere shape.
Can someone help me with this problem?
EDIT
This is my plot in maple. And as you can see, it doesn't have a spherical shape.
But I think I figured it out. It's just the scaling that's messed up. If I used the scaling=constrained command I end up with this:
Which looks much better!
So this is what I get when I plot what you prescribed.
''' SphericalPlot3D[{1}, {[Theta], 0, Pi/2}, {[Phi], 0, 3 Pi/2}] '''
And I am plotting in Mathematica. It is part of a sphere, where is the problem?