# Sphere/hemisphere

• Dec 12th 2010, 02:39 AM
SyNtHeSiS
Sphere/hemisphere
Sketch $\sqrt{13 - x^2 - y^2}$

Attempt:

$z^2 = 13 - x^2 - y^2$

$z^2 = -x^2 - y^2 + 13$

$x^2 + y^2 + z^2 = 13$

Now I dont understand why this is half of a sphere (which opens up downwards) and not a whole sphere?
• Dec 12th 2010, 02:43 AM
Prove It
If this was $\displaystyle z = \sqrt{13 - x^2 - y^2}$, this is really $\displaystyle z = +\sqrt{13 - x^2- y^2}$, which is the upper half of the sphere.

To be a full sphere it would need to be $\displaystyle z = \pm \sqrt{13 - x^2 - y^2}$.