Jessica Furr

EMT 468

October 6, 1996

Assignment for Day 3 - Detailed Lesson Plan on Topic Covered

The following notes are meant to be used with the accompanying figures in "cylinder," a Cabri file. This lesson introduces the formula for the volume of a cylinder by deriving the equation from the presumably familiar task of finding the volume of a rectangular prism. The sketches in Cabri are only preliminary figures. An effective presentation of this lesson would include several various copies of the figures with certain segments or perimeters highlighted in a different color to focus the students' attention on the characteristics being discussed. Also, the tabulation of radii, lengths, areas, and volumes is discussed in these notes as a useful example. In order to actually use this, I would need a great deal more famliarity with how to make that table feature in Cabri do what I want. The figures are constructed so that lengths and radii are easily changed by stretching the corresponding segment. The cylinder is constructed using ellipses for visual effectiveness. Students should be reminded that the figure is meant to represent a cylinder with circular bases. The formula for the area of the base does not calculate the area of the ellipse, but is equal to one-half of the major axis, squared, times pi. The segment corresponding to half the minor axis should be hidden during presentations. The prepared answers for area and volume can be left on screen, since the purpose of the exercise is not to find the volume, but to figure out how it is obtained.

Introduction:

Can You Deduce a Formula for Finding the Volume of a Cylinder?

I. Notice all the information that is given. (see picture of cylinder)

A. Make a table of what is given - radius, height, area of circle, volume

B. Include knowledge you bring to the situation - value of pi, formula for area of circle = pi times radius², anything else offered by students.

II. Adjust the height of the cylinder.

A. Does this affect the volume?

B. Can we conclude that H will be a factor in our equation?

III. Let's compare our current situation to finding the volume of a rectangular prism. (see picture)

A. How do you normally find the volume of a prism?

i. Make a table with length, width, height, and volume.

ii. State the formula, l*w*h = V

B. We don't know the formula for the cylinder yet, but we decided that it looks like: V= h*?

(here would be a good place to show rectangle and cylinder side by side with heights color-coordinated)

C. If the heights are comparable in each case, then "?" should somehow relate to "l*w"

D. How might we describe "l*w"? - BASE of figure

E. What is the BASE of the cylinder? - CIRCLE

(here you should show side by side figures with bases color-coordinated)

F. What kind of information do we want about the circle? Remember, it's like the base of the rectangle. - AREA

IV. Now, the formula for the area of a circle has been given- pi*radius². Can we put it all together?

V. Compare:

Volume of Rectangular Prism = Base * Height = l*w*h

Volume of Cylinder = Base * Height = pi*r²*h