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Find the volume common to two circular cylinders, each

with radius $r,$ if the axes of the cylinders intersect at right

angles.

$$

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

$$

Applications of Integration

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Harvey Mudd College

Baylor University

University of Nottingham

Boston College

{'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"}

University of California, Berkeley

Applications of Integration