Just rotate the part of the circle between y = r - h and y = r around the y-axis:Can someone help me out on this problem?
We are supposed to find the volume using integrals. Meaning as x or y changes, the cross-sectional area will change, so we find the equation for the cross sectional area, and then take the integral of it across the height.
In this one, I figured the cross-sectional area =
And if we set the bottom of the blue section along the x-axis, then it would be integrated from 0 to h, so
But somehow I'm supposed to incorporate the radius.
Back of the book says the answer is
edit: well, part of my problem, I think is that I should be puting the cross-sectional area in terms of y. And I think I should be using the equation of a circle: x^2=r^2-y^2. That still doesn't get me the right answer, but it's much closer to theirs, as this would become so getting closer :/ But this method seems like it would integrate just the top half of the circle. So somehow I need to remove that gap between the circle's center, and the bottom of h.