cp /math/calclab/MA1024/Coords_start_D10.mws ~/My_Documents

Another way to access the getting started worksheet is to go to your computer's Start menu and choose run. In the run field type:

\\toaster\calclabwhen you hit enter, you can then choose MA1024 and then choose the worksheet

Coords_start_D10.mwsRemember to immediately save it in your own

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 for a circular cone:

**A)**- Graph the equation using the domain values of , and the range values .
**B)**- Find the equation of the cone in cylindrical coordinates and then graph the equation. Write the equation in text in its simplest form.
**C)**- Find the equation of the cone in spherical coordinates and graph it. Write the equation of the equation in text in its simplest form.
**D)**- Use rectangular coordinates and a triple integral to find the volume of this circular cone with height . Now repeat this using cylindrical coordinates. Which method is easier?

- Now suppose an ice cream cone is bounded below by the same equation of the cone given in exercise 1 and bounded above by the sphere . Find the volume of the ice cream cone using a triple integral in cylindrical coordinates and again using spherical coordinates. Include a plot of the ice cream cone.

2010-04-27