Answer:
[tex]x^2 + y^2 + z^2 \le 25[/tex] for [tex]z \ge 0[/tex]
Step-by-step explanation:
Given
[tex]r = 5[/tex] --- radius
Required
Determine the inequality of the region
The inequality of a region of a sphere is determined using:
[tex]x^2 + y^2 + z^2 \le r^2[/tex]
Substitute 5 for r
[tex]x^2 + y^2 + z^2 \le 5^2[/tex]
[tex]x^2 + y^2 + z^2 \le 25[/tex]
Solving further: The question says only the upper hemisphere is considered.
This implies that:
[tex]z \ge 0[/tex]
So, the equation is:
[tex]x^2 + y^2 + z^2 \le 25[/tex]
[tex]z \ge 0[/tex]
