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Volume of a sphere

by Feodalherren
Tags: sphere, volume
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Feodalherren
#1
Jun23-13, 03:19 PM
P: 323
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?!
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D H
#2
Jun23-13, 03:29 PM
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P: 15,065
What's the area of a circle of radius r? What if the radius is y instead of r?
Mark44
#3
Jun24-13, 12:50 AM
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P: 21,216
Quote Quote by Feodalherren View Post
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
Probably a typo - the volume is (4/3)##\pi r^3##.

Quote Quote by Feodalherren View Post

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?!
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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