Q. Find the volume of the smaller wedge cut from a circular cylinder of radius r by two planes whose line of intersection is a chord at distance b from the axis of the cylinder, if the wedge has thickness c at its thickest point.
Struggling with this question, have done the question when the two planes intersect at the axis, but when it come to integrating at the at a distance from the axis the solution become more complicated.
There is a solution using Trig. I am sure, but it's not asking for that. Feel as if there is a piece of geometry that I am missing which give a simpler solution. If you can help please do, Thanks
The blue rectangle has a width of $2\sqrt{r^2-(b+x)^2}$ and a height $\displaystyle h={cx\over r-b}$. The volume of the wedge is thus $$ \int_0^{r-b}2\sqrt{r^2-(b+x)^2}{cx\over r-b}dx. $$