Question

Write an inequality to describe the region. The solid upper hemisphere of the sphere of radius 5 centered at the origin

Answer 1

Answer:

$x^2 + y^2 + z^2 \le 25$ for $z \ge 0$

Step-by-step explanation:

Given

$r = 5$ --- radius

Required

Determine the inequality of the region

The inequality of a region of a sphere is determined using:

$x^2 + y^2 + z^2 \le r^2$

Substitute 5 for r

$x^2 + y^2 + z^2 \le 5^2$

$x^2 + y^2 + z^2 \le 25$

Solving further: The question says only the upper hemisphere is considered.

This implies that:

$z \ge 0$

So, the equation is:

$x^2 + y^2 + z^2 \le 25$

$z \ge 0$