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Problem 46 Hard Difficulty
Use cylindrical shells to find the volume of the solid.
The solid torus of Exercise 6.2.63
Answer
2$\pi^{2} R r^{2}$
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Topics
Applications of Integration
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Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Michael J.
Idaho State University
Joseph L.
Boston College
Watch More Solved Questions in Chapter 6
Video Transcript
we have been instructed to use cylindrical shells, which means we have something looking like this. We have our capital. Are we ever Laure kissed there? Which means we have to calculate the volume of two pi times capital R times, the radius times of high times d of X. So in this case, we know we're gonna be doing square root of R squared minus X squared detox minus two pi times the integral from negative or are axe Times Square are squared minus X squared D x, which gives us two times capital are times pi times 1/2 pi r squared times to pied time zero which is obviously gonna be zero because when we put in the zero, let me just get zero which is capital are times pi r which is squared, which is our solution because remember, we had a symmetric and travel and the problem, which was why we had a zero value. Because if you look at this, you'll see the circle is where the circles us symmetrical on both sides because, remember were using cylindrical shells for this question. So this expanded out is to pi squared capital are lower case R squared
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Michael J.
Idaho State University
Joseph L.
Boston College
