Work out the area of this circle. Give your answer in terms of pi and state its units.

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  36π mm²

Step-by-step explanation:

You know that (ab)² = a²b². This tells you that ...

  πr² = π(6 mm)² = π(6² mm²) = 36π mm²

The units of area are square millimeters (mm²).

Additional comment

For a variety of reasons, I find it is often helpful to keep units of measure with the associated number. It serves as a check on the arithmetic, among other things. If the units don't make sense, chances are good that the math doesn't make any sense.

It should be fairly obvious that if linear dimensions are in millimeters, then the corresponding area dimensions will be square millimeters. (Volume will be cubic millimeters.)

In the math, the units can be treated in the same way as any other variable. This tells you, for example, that you can only add (or subtract) measures with the same units (like terms). Division can be used to cancel same units, or to get from volume to area, for example (mm³/mm = mm²).