

Cylinders
and Scale
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4  5
Tape sample cylinders of each size to your class chart. These will make
the chart numbers more meaningful and guard against the problem of disconnecting
the numbers from what they represent. Referring to your chart on the chalkboard,
discuss the way that the linear measurements grow slowly, while the surface
dimensions and volume grow more rapidly.
To grow larger cylinders, you change two linear dimensions: the height
and the circumference (or diameter of the base).
Cylinder
# 
Height
of Cylinder
(h) 
Diameter
of base
(d)

Circum
ference of base
(c)

Area
of base

Area
of cylinder surface
(can
surfaces)

Volume
(cans) 
1 
1 
1 
1 

1 
1 
2 
2 
2 
2 

4 
8 
3 
3 
3 
3 

9 
27 
4 
4 
4 
4 

14 
64 
5 
5 
5 
5 

25 
125 
... 
... 
... 
... 
... 
... 
... 
Instead of increasing all
dimensions, try making cylinders with just double the height. Ask what
happens to the volume (it doubles). Now try making a cylinder with double
the circumference or diameter. Ask what happens to the volume (it is four
times as big). Doubling the height doubles just one dimension of the cylinder.
Doubling the circumference is like doubling the perimeter of the base
on a cube. It doubles the length and width and increases the area of the
base by four times. Also try tripling, quadrupling, etc., the height or
circumference.
