Finding domains of 3d quadratic surfaces

[DottZakapa]

Homework Statement

$z^2\leq x^2+y^2, z\geq x^2+y^2$

Relevant Equations

domain

$z^2\leq x^2+y^2, z\geq x^2+y^2$
I know the shapes of those inequalities, but the question is:
How do i find if the point are external the shape or internal?

 

[member 587159]

Take a simple test point and see if its coordinates satisfy the inequalities.

 

[DottZakapa]

Take a simple test point and see if its coordinates satisfy the inequalities.

in the case of the cone any number satisfy the inequality, but what if i want the external points of the cone

 

[Mark44]

in the case of the cone any number satisfy the inequality, but what if i want the external points of the cone

That's not true about the cone. For example, the point (1, 1, 2) is outside the cone.