Question

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

Answer 1

Answer:

  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)