Write an inequality to describe the region. The solid upper hemisphere of the sphere of radius 9 centered at the origin

z ≤ √ (81 - x² - y²)

Step-by-step explanation:

If the sphere is described in 3-D coordinates as ...

x² + y² + z² = r²

Then the upper surface is ...

z = √ (r² - x² - y²)

With r=9, the solid volume below that surface and above the x-y plane is ...

z ≤ √ (81 - x² - y²)