💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Oh no! Our educators are currently working hard solving this question.

In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics.



Numerade Educator



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.


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


You must be signed in to discuss.

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