## Related questions with answers

Question

Write inequalities to describe the region. The solid upper hemisphere of the sphere of radius 2 centered at the origin

Solutions

VerifiedSolution A

Solution B

Answered 1 year ago

Step 1

1 of 2$x^2 + y^2 + z^2 \leq 4$ is the solid sphere with radius 2 centered at the origin. However, since the problem says it's only the upper hemisphere, therefore, $z \geq 0$. Therefore, the answer is:

$x^2 + y^2 + z^2 \leq 4 \text{ where } z \geq 0$

Answered 1 year ago

Step 1

1 of 2Note that the region is only the upper hemisphere of a sphere centered at the origin and with radius 2. Since z-axis is the vertical axis, this means that the sphere only consists of points with $z \geq 0$.

Thus, by following the equation of a sphere centered at the origin, we have:

$x^2+y^2+z^2 \leq 4, z \geq 0$

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