Cylinders and Scale

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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.