Volume of a sphere

  1. 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.

    [​IMG]

    So I get lost where it starts talking about a cross-sectional area all of a sudden multiplying by ∏. What's going on here?!
     
  2. jcsd
  3. D H

    Staff: Mentor

    What's the area of a circle of radius r? What if the radius is y instead of r?
     
  4. Mark44

    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.
     
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