# Example on spherical coord. and trip. integral

1. Nov 29, 2007

### hotcommodity

[SOLVED] Example on spherical coord. and trip. integral

1. The problem statement, all variables and given/known data

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 $$\delta$$ is bounded by the spherical surface with equation $$\rho = a$$. Use spherical coordinates to compute its volume V.

It says that the bounds are:

$$0 \leq \rho \leq a, 0 \leq \phi \leq \pi, 0 \leq \theta \leq 2 \pi$$

The bounds for $$\phi$$ confuse me. Why does it go from 0 to pi? Wouldn't that only account for half of the sphere?

Any help is appreciated.

2. Nov 29, 2007

### Dick

One angular coordinate measures pole to pole angle, that goes from 0 to pi. The other measures the equatorial angle, that goes 0 to 2pi. Together they cover the whole sphere.

3. Nov 30, 2007

### HallsofIvy

Staff Emeritus
Draw a picture. If $\phi> \pi$ you would be picking up the same points as with $\phi< \pi$, $\theta> \pi$.

4. Nov 30, 2007

### hotcommodity

Oh ok, I get it, as theta goes from 0 to 2pi, phi sweeps the entire sphere. Thank you both.