- This exercise is intended to familiarize you with the
procedures
`revolve`,`RevInt`,`LeftDisk`and`LeftInt`as an approach to approximating the volume of a solid of revolution using the disk method. Apply the four commands as listed above to the function**f**defined by on the interval with**n=10**. Your answer should include the two numerical values and references to the two 3-dimensional plots. - The formula for the volume of a cone, namely,
can be obtained by assigning the points , , and
as the vertices of a right triangle and rotating that triangle about
the
**x**-axis.- Following a similar approach as above, derive the formula for the volume of a frustrum of a cone. That is, a cone with the top cut off parallel to the base.
- Show that your formula can be expressed in the traditional handbook form: , where and are the areas of the two bases.

- A torus - a solid shaped like a doughnut - is generated by
revolving a circle about an axis that does not intersect the circle.
By rotating the circle about the line
**y = 3**, print a plot of the torus which depicts its doughnut-like image and compute its volume. Your answer should include the numerical value for the volume and a reference to the 3-dimensional plot. - A glass container is fashioned acording to the image obtained by
rotating the graph of the function
**g**defined by on the interval and**x**measured in centimeters.- Obtain a plot of the the container in an upright position. Be sure to reference your plot.
- Determine the capacity of the container if filled to the brim.
- It is decided that Herky the minnow is to be allowed to use the container as a fish bowl. When Herky is placed in the container when it is filled to a depth of 4 cm, the depth increases to 4.5 cm. If the water weighs 1 gm/cm, how much in ounces does Herky weigh?

Wed Dec 6 09:46:40 EST 1995