1. The problem statement, all variables and given/known data Show that the volume of a sphere of radius r is V = (4/3)πr^2 2. Relevant equations calculus, integration 3. The attempt at a solution I have the solution in the book but it's confusing me, I'll attach a picture. So I get lost where it starts talking about a cross-sectional area all of a sudden multiplying by ∏. What's going on here?!
Probably a typo - the volume is (4/3)##\pi r^3##. The book is using disks that are oriented vertically (the x-axis intersects each disk perpendicularly). The volume of such a disk is its area times its thickness, dx.