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The volume should not change if the cylinder is rigid.
There are many "attributes" of a cosine function. Some examples of attributes are as follows: For, constants a, b, n, y=a*cos(nx)+b has an amplitude of a, a period of 2pi/n, a range of [-a+b,a+b], a derivative of y'=-an*sin(nx).
you do some multiplication
People think about a cylinder as closed, and so the solids, or faces, that it has are on the bottom and top. Those two circles are the only faces in a cylinder. Examples: a soup can, some types of jars, candles (some).
The size and orientation of the shape remain unchanged.