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# Find the volume of the described solid $S .$A cap of a sphere with radius $r$ and height $h$

## $\frac{1}{3} h^{2} \pi(3 r-h)$

#### Topics

Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

{'transcript': "the problem is finding the volume of the described solid as a cap of a sphere with writers are on DH hat each. So look at the graph here. This is a cap of a sphere. So if I did not the ride years was a bass is equal to a then a squire is cultural r squared minus arm minus H square. This is a cultural to R H minus JJ Square. So for me, cross section off this cab. It is that disk. So if any note area of the cross section is a why you're why is the distance between this two trains this transaction on the base we have a wild horse high a squire. This's cultural H minus y over h squared. Then the volume of this cab three two into grow from zero to age. You know why you are This is Echo two. Hi. A squire into girl from zero to age H minus y were H square. You know why? So the answer is this is Nico too. H hi over three Ma'am, stay square. This is Echo two Ej pi. Over three times you are H minus. EJ scored"}

WZ

#### Topics

Applications of Integration

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp