Volumes of Known Cross Section
This worksheet is intended to demonstrate the Calculus I or AP Calculus AB concept of calculating a volume of known cross section.
Drag points A and B on the x-axis in the left graphics window to determine the start and stop of the volume in the x direction. If they don't click/drag smoothly, consider selecting one of them and using the arrow keys on a keyboard to adjust values.
You may enter bounding functions f(x) and g(x) into the input fields or just drag the existing graphs in the Graphics1 window.
Drag the n slider to determine the number of evenly-spaced cross sections displayed.
When n is set to 0, a single cross section is displayed, and its position is determined by point C on the x-axis.
- For “rectangle,” the “ratio” = (height out of xy-plane)/(base in xy-plane)
- For “triangle” (isosceles), the “ratio” = (length of congruent sides out of xy-plane)/(length of side in xy-plane)