The Surface Area of a Cylinder

Edwina R. Justice              Gunsaulus Scholastic Academy
                               4420 South Sacramento Ave.
                               Chicago IL   60632
                               (312) 535-7215

Introductory Comments:

This is a description of a phenomenological approach presentation. It 
is an extension of a mini-teach, "The Area of a Circle", presented in 
the Summer of 1986. 

Objectives:

A. To relate the areas of one rectangle and two circles to the 
   total surface area of a cylinder.
B. To relate the circumference of a circle to the base of the 
   rectangular section of a cylinder.
C. To review the area of a circle.

Apparatus Needed:

A. Round container lids with varying circumferences
B. Rectangles, cut from flexible material, with bases corresponding to 
   the circumferences of the lids.  Allow one inch for overlapping the 
   ends.  Mark this one inch space.
C. Circles cut to match the sizes of the lids.
D. Measuring instruments.
E. Tape

Recommended Strategy: 

This lesson has been designed for groups.  The format of the group
report should include a topic, figures (labeled appropriately), 
procedure and conclusions. Materials should be distributed only when 
needed.  The recommended order of activities is listed below.

A. Review concepts from "The Area of a Circle"
  1. circumference
  2. diameter
  3. c/d = pi   c = pi*d
  4. pi is approximately 3.14 or 22/7
  5. c = 2pi*r

B. Calculate the area of the rectangle
  1. Label base, height
  2. Measure and compute area using A = bh

C. Make circular form
  1. Overlap the ends of the rectangle and tape them together
  2. Place the form on the corresponding lid
  3. Discuss the apparent shape

D. Relate the base of the rectangle to the circumference of the lid

E. Place second circle on top of the form and discuss results 

F. Remove second circle and tape

G. Label base as circumference

H. Calculate area of rectangle using C = pi*d for the base of the 
   rectangle 

I. Compare the results of the two computations of the area of the 
   rectangle

J. Calculate the area of two circles

K. Add the area of the two circles to the area of the rectangle

L. Write group report

This series of activities has been designed to guide students to an 
understanding of the components of the cylinder surface area formula.  
As students proceed with the construction of the cylinder, they should 
relate its form to the flat surfaces of a rectangle and two circles.  
The area of the two circles can be computed by multiplying pi times 
radius squared and that quantity times 2. In the surface area formula 
the process appears as 2pi*r2.  The use of the lid and a second circle 
which is the same size as the lid should be related to the use of the 
constant 2 in this part of the formula.  The different processes  for 
computing the area of the rectangle should be related to 2pi*r*h.  
Discussion of the constant 2 in this part of the formula may be made at 
the time c = pi*d is used to compute the area of the rectangle.  It is 
necessary for students to relate 2 radii to one diameter.