cp /math/calclab/MA1024/Coords_start_D11.mws ~/My_Documents

You can copy the worksheet now, but you should read through the lab
before you load it into Maple. Once you have read to the exercises,
start up Maple, load
the worksheet `Coords_start_D11.mws`, and go through it
carefully. Then you can start working on 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 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 a right circular cone of 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 spherical coordinates. Include a plot of the ice cream cone.

2011-04-25