"The Surface Area of a Cylinder" (Version 2.0)
Return to Mathematics Index
Edwina R. Justice Gunsaulus Scholastic Academy
4420 South Sacramento Ave.
Chicago IL 60632
This is a description of a phenomenological approach presentation. It is an
extension of a mini-teach, "The Area of a Circle" (1986) and a PA, "The Surface Area
of a Cylinder" (1988). A problem-solving situation, which requires the use of the
two concepts, was formulated.
1) Use a phenomenological approach to problem-solving.
2) Apply concepts to problem-solving situation.
3) Participate in group activity.
Tape (masking or scotch)
Round container lids (different circumferences)
Paper circles (equal circumferences)
Rectangles with different dimensions (measure of base should be equal to measure of
circumference of a corresponding lid)
Cut two circles with equal diameters and one rectangle from cm. grid paper.
Measure of base of rectangle should correspond to measure of circumference of one
circle. These figures should be used to make a worksheet which can be distributed to
Form small groups and measure circumference and diameter of several lids.
Divide circumference by diameter for each lid.
Discuss constant (pi) that results when circumference is divided by diameter.
Use paper circles to show A = pi(r2). (This procedure is explained in SMILE, 1986.)
Calculate areas of figures on worksheet.
Cut figures and make a cylinder.
Relate areas of plane figures to surface area of resulting cylinder.
Use rectangles and lids to make several other cylinders.
Calculate the surface areas of the cylinders (Use area of each rectangle plus two
times area of corresponding lid).
Discuss related equations:
Area of rectangle section of cylinder = base * height
circumference of lid * height
Circumference = pi(d)
Diameter = 2r
Diameter = c/pi
Develop formula for surface area of cylinder:
Area = (2(pi)r2) + (2(pi)rh)
Review use of 2 as a constant in equation:
2(pi)r2 (two represents two circles)
2(pi)rh (two represents two radii or one diameter)
Two rectangular sheets 20 cm. by 24 cm. and 15 cm. by 30 cm. are to be rolled
to form cylinders. What is the height and diameter of the cylinder with maximum
surface area that can be formed using either of these sheets?
Construct the cylinder with maximum surface area (with lids).
Report results to class.