Our Discord hit 10K members! 🎉 Meet students and ask top educators your questions.Join Here!

Like

Report

FS
Numerade Educator

Like

Report

Problem 50 Easy Difficulty

Find the volume common to two circular cylinders, each
with radius $r,$ if the axes of the cylinders intersect at right
angles.

Answer

$$
\frac{16 r^{3}}{3}
$$

Discussion

You must be signed in to discuss.

Video Transcript

{'transcript': "All right, So for this push in, we know that we have to find the volume that is common to circular cylinders, that we don't have a volume. The cylinder is pi r squared h each with radius are so we can rewrite this. Everyone is equal to pi r One squared h B two is pi r two squared h if the axis of the cylinders intersect at right angles. All right, so therefore the cylinders have to be let's see, like, sort of perpendicular to one another, right? And we have to find the volume that is common to the two of them. So that is the intersection volume right there. So if we take the integral off where they intersect, that's pi r two squared h is equal. I are one squared h find their intersection one, we'll call them A and B taking into go between and be off. Hi are one squared h if we're going to square, this minus high are two squared h squared d r. And that's your final answer"}

FS
University of California, Berkeley
Top Calculus 2 / BC Educators
Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Joseph L.

Boston College