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Numerade Educator

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Problem 45 Hard Difficulty

Use cylindrical shells to find the volume of the solid.

$ A $ sphere of radius $ r $

Answer

$\frac{4}{3} \pi r^{3}$

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Video Transcript

okay, we know we're gonna be using the formula to pi. Times are bounds from A to B, which in this case is ear to our of x times f of x So acts times are off of axe is R squared minus X squared times dx To solve this integral we know that if you is r squared minus x squared that our acts detox is gonna be negative 1/2 d'you Which means plugging back in tour formula. We have two pi times the inter girl from R squared to zero of negative 1/2 you to the 1/2 d'you which gives us negative pie. Now we're integrating. Using the power rule increased the expert by one divide by the new exponents. Remember the bounds get flipped when you have a negative u substitution, as we had in this problem, we end up with 2/3 pi r cubed, however, were not done. We need to multiply this by two because we only have half of what we need toe end up with our volume is 4/3 pi r cubed