- #1
hotcommodity
- 436
- 0
[SOLVED] Example on spherical coord. and trip. integral
Here's the example in the book. They're proving the volume of a sphere using spherical coordinates.
A solid ball T (the region) with constant density [tex]\delta[/tex] is bounded by the spherical surface with equation [tex]\rho = a[/tex]. Use spherical coordinates to compute its volume V.
It says that the bounds are:
[tex]0 \leq \rho \leq a, 0 \leq \phi \leq \pi, 0 \leq \theta \leq 2 \pi[/tex]
The bounds for [tex]\phi[/tex] confuse me. Why does it go from 0 to pi? Wouldn't that only account for half of the sphere?
Any help is appreciated.
Homework Statement
Here's the example in the book. They're proving the volume of a sphere using spherical coordinates.
A solid ball T (the region) with constant density [tex]\delta[/tex] is bounded by the spherical surface with equation [tex]\rho = a[/tex]. Use spherical coordinates to compute its volume V.
It says that the bounds are:
[tex]0 \leq \rho \leq a, 0 \leq \phi \leq \pi, 0 \leq \theta \leq 2 \pi[/tex]
The bounds for [tex]\phi[/tex] confuse me. Why does it go from 0 to pi? Wouldn't that only account for half of the sphere?
Any help is appreciated.