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I don't really understand what these two questions are asking. Nor do I know how to start it.

1) Describe in words the region of $\mathbb {R}^3$ represented by: $x^2 + z^2 \le 9$.

2) Write an inequality to describe: The solid upper hemisphere of the sphere of radius 2 centered at the origin.

Can some please explain what I am supposed to do here? Thanks in advance.

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For $1$, the region of space satisfying that inequality will look like a familiar shape. Can you figure out what shape? –  Alex Becker Aug 25 '12 at 23:51
    
Depends on which way is up. They probably mean that up is $z\ge 0$. –  André Nicolas Aug 25 '12 at 23:59

1 Answer 1

up vote 3 down vote accepted

For question no. $1$, notice that if we plot $x^2+z^2 \le 9$ in $\mathbb R^2$, we get a filled circle of radius $3$. Add another axis, and what happens? For example, a plate is a circle, but what 3d shape is made when plates are stacked?

For question no. $2$, recall that an (empty, i.e. not solid) sphere of radius $r$ has the equation $x^2+y^2+z^2=r^2$. Noting that the radius is $3$, we have $x^2+y^2+z^2=9$. How do we now make this sphere filled? Look at what was done in question $1$ to make a filled circle.

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I'm sorry. Could you explain this a little more. I'm still kind of lost with this problem. –  Avalon-96 Aug 29 '12 at 0:04
    
@Avalon-96 Edited. Is it still unclear? –  Argon Aug 29 '12 at 0:35
    
Ah, yes, that makes more sense. Thank you. –  Avalon-96 Aug 29 '12 at 1:40

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