(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider two quarters of a cylinder of radius R. What is the volume of a the intersection of a two quarters of two cylinders if the quarters meet at a right angle? Two sides of the bounded region will be rectangular according to this arrangement. (see the diagram when it gets approved)

2. The attempt at a solution

I need to do this in Cartesian coordinates so here goes

let the Z axis be straight up, the X axis out of the page an the Y axis parallel to the page.

For the cylindrical part parallel to the X axis

[tex] V = \int_{0}^{r} dx \int_{0}^{r} \int_{0}^{\sqrt{r^2 - y^2}} dy dz [/tex]

For hte cylindrical parallel to the Y axis

[tex] V = \int_{0}^{r} dy \int_{0}^{r} \int_{0}^{\sqrt{r^2-x^2}} dx dz [/tex]

And the find the volume i need to subtract the above two??

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# Homework Help: More volume

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