# Volume of a sphere

1. ### Feodalherren

455
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?!

### Staff: Mentor

What's the area of a circle of radius r? What if the radius is y instead of r?

### Staff: Mentor

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.