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Problem 47 Hard Difficulty

Use cylindrical shells to find the volume of the solid.

$ A $ right circular cone with height $ h $ and base radius $ r $

Answer

$\frac{1}{3} \pi^{2} h$

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Video Transcript

using cylindrical shows implies that we have the region bounded on the top with wise h and on the bottom with why is h over? Our times acts. So in other words, we have height is H minus h over our times acts radius is X, which means RV is two pi times integral from zero to our times radius which is acts times height which is a TSH minus h over our times acts D x which expect which simplifies to two pi h again you can Paul all the Constance to make it more simple fired like this. Now we can integrate using the power rule which means be increased the exponents by one divide by the new exponents. Now we can plug end, we end up with 1/3 pi r squared times each.

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