(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://staff.washington.edu/dhlee528/003.JPG [Broken]

2. Relevant equations

x = r sin ( phi) cos ( theta)

y = r sin ( phi )sin (theta)

z = r cos ( phi )

3. The attempt at a solution

[tex]

vol=8 \int_0^\frac{\pi}{2}\int_0^\frac{\pi}{2}\int_0^r \rho^2 \sin(\phi)d\rho d\theta d\phi

[/tex]

[tex]

8 \int_0^\frac{\pi}{2}\int_0^\frac{\pi}{2} \sin(\phi)(\frac{\rho^3}{3}){|}_0^r d\theta d\phi

[/tex]

[tex]

\frac{4r^3 \pi}{3}\int_0^\frac{\pi}{2}sin(\phi)d\phi

[/tex]

[tex]

-\frac{4r^3\pi}{3}[0-1]=\frac{4\pi r^3}{3}

[/tex]

I think I got spherical coordinate right but don't know how to do for rectangular or spherical coordinate

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof of Volume of a ball

**Physics Forums | Science Articles, Homework Help, Discussion**