Calculating the Volume of a Vase
You are to determine the
volume of the vase pictured here. The photograph on the right shows the construction
of the vase and that its height is 50 cm.
Unlike practice problems
from textbooks, most real life problems involve "messy" coefficients.
Even if the function is easy to antidifferentiate, the arithmetic is usually
In this lesson
you will learn to...
- Capture the coordinates of
points along the edge of the vase from its photograph
- Use those points and your
calculator to determine a function
- Set up the definite integral
for the volume of the vase (a solid of revolution) using your function
(need help? disk
method for calculating volume)
- Evaluate the integral using
You may already know how to perform
some of these. We have provided links to refresh your memory if needed.
Use the applet
to find the coordinate values for the edge of the vase
- Click anyplace on the image
to move the cursor to that point.
- Notice the readout at the upper
right gives the location of the cursor measured in pixels from the
lower left corner of the image.
- You can fine tune the location
of the cursor by clicking on the four arrows at the left, right, top,
and bottom of the map.
- Each click moves the cursor
one pixel in the direction indicated by the arrow.
- Click the blue button, labeled
"Mark point," to record the coordinates of a point.
- Click it each time that you
have moved the cursor to a new point whose coordinates you want to
- Click the red button, labeled
"List points," to display the coordinates of the points
whose coordinates you have recorded.
- A new window will appear with
the information that you have recorded.
- If necessary, click the black
button, labeled "Clear points," to clear the list of recorded
points and begin again.
Now that you have coordinates from the applet,