\\filer\calclab

when you hit enter, you can then choose MA1024 and then choose the worksheet

Coords_start_C14.mw

Remember to immediately save it in your own home directory. Once you've copied and saved the worksheet, read through the background on the internet and the background of the worksheet before starting the exercises.

To change to cylindrical coordinates from rectangular coordinates use the conversion:

To change to spherical coordinates from rectangular coordinates use the conversion:

Using a triple integral to find the volume of a solid translates in the following manner:

- Given the rectangular equation:

**A)**- Graph the equation using the domain values of , and the range values .
**B)**- Find the above equation in cylindrical coordinates and then graph the equation. Write the equation in text in its simplest form.
**C)**- Find the above equation in spherical coordinates and graph it. Write the equation of the equation in text in its simplest form.
**D)**- Looking at the three equations, which coordinates appear to give the simplest equation?

- Given the rectangular equation:

**A)**- Graph the equation using the domain values of , and the range values .
**B)**- Find the above equation in cylindrical coordinates and then graph the equation. Write the equation in text in its simplest form.
**C)**- Find the above equation in spherical coordinates and graph it. Write the equation of the equation in text in its simplest form.
**D)**- Looking at the three equations, which coordinates appear to give the simplest equation?

- Use a triple integral in all three coordinate systems to prove that the volume of a sphere of radius centered at the origin is
. You will need to use the command
`value`instead of`evalf`.

2014-02-24