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Problem 40 Easy Difficulty

The solid cylinder that lies on or below the plane $ z = 8 $ and on or above the disk in the $ xy $-plane with center the origin and radius 2.

Answer

$0 \leq z \leq 8, x^{2}+y^{2} \leq 4$

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Video Transcript

we want to describe the region, which is the solid cylinder that lies on or below the plane. Z equals age, an honor above the disc and the X Y plane with center, the origin and radius, too. So in the X Y plane, the disc with center at the origin radius, too, just described by well, you have. The boundary circle is expert plus y squared equals the radius squared four. So if you let X squared plus y squared your radius, either equal for or be less than it. Then you get the solid disc in the X Y plane, though in our three, this is no the solid cylinder, which extends infinitely in the Z direction in both ways, but we want to be to be between zero and eight, so we and forced see between 08