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Problem 37 Easy Difficulty

Describe in words the region of $ \mathbb{R}^3 $ represented by the equation(s) or inequality.

$ x^2 + z^2 \le 9 $

Answer

solid circular cylinder with radius 3 with the $y$ -axis as its axis

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Video Transcript

what region in space is described by the inequality X squared plus C squared is less than or equal to non. Whatever that region is is gonna have a boundary given by the related equation X squared. Plus, the square equals nine and two dimensions in the XY plane. That would be a circle with Radius three. But if why it could be anything, then this extends the circle into a cylinder center at the with the Y axis. That's the boundary, and it's included in this region because the inequality defining it is less than or equal to its the or equal to part. If we're also looking for points where expert policy squared is less than nine, we're also talking about the interior of that cylinder, and so the region is a sir cure cylinder of Radius three centred at the Y axis, and it's interior. Some places might call that a circular, a solid circular cylinder to indicate that it's not talking just about the boundary of it, but its interior as well