Question

The diameter of a circle is 2 centimeters. What is the length of a 180° arc?

Give the exact answer in simplest form.
I centimeters
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Answer 1

The length of the arc is:
`\pi\,\,cm\approx\,3.14\,\,cm`

Explanation:

Notice that a circle of diameter 2 cm has radius 1 cm (half of the diameter).

Also notice that the length of the full circle (which corresponds to a
`360^o` arc, is the circumference length given by the known formula
`2\,\pi \, R`, so the arc subtended by half such angle (that is a
`180^o` angle would be:
`(2\,\pi \, R)/(2) = \pi \, R`

Therefore with this info we get that:

the length of this 180° arc for a radius of 1 cm is =
`\pi \, R= \pi\,1\,cm=\pi\,\,cm\approx\,3.14\,\,cm`