Quandaries and Queries

Hi can you help me with my homework please?
Is a cylinder a type of prism?

From Rebecca

Hi Rebecca,

At times we have to be very careful with language. Before we look at the word prism I have to make sure that we agree on the word cylinder. I assume that your cylinder has a circular cross-section, like a soup can or the cardboard tube in the center of a roll of paper towels.

If this agrees with your meaning of cylinder then a cylinder is not a prism. Here is the definition of prism from the Oxford English Dictionary

Geometry: A solid figure of which the two ends are similar, equal, and parallel rectilineal figures, and the sides parallelograms. "Similar, equal, and parallel rectilineal figures" means that the two ends (bases) have to be
  1. "parallel", which they are in your cylinder,

  2. "similar and equal", which they are in your cylinder, they are identical circular disks

  3. "rectilineal figures". This is not true for your cylinder. Rectilineal means that the base has to have edges that are straight lines, like a triangle, square or pentagon. A circle is not a rectilineal figure.

The definition of prism also says that the sides have to be parallelograms. The "side" of your cylinder is tube shaped, it is not made up of parallelograms.

I hope this helps,

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