A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which students have to choose the value that most closely estimates the circumference of a circle, given its radius and a value to use for π.

The diagram looks something like this:

We are asked to choose the value from four options that is closest to the circumference of the circle, using 3.14 for π. This problem involves a main skill (applying a formula) and a secondary skill (estimating). Here, we take “estimating” to mean rounding, which is not really an estimation skill after all, leaving us with only a main skill of applying the formula for circumference of a circle given the radius and a value for π.

If you don’t know the formula, this problem was lifted from a statewide test, and formula sheets are provided by the state. Whether you know it by heart or get it from the formula sheet, the circumference of a circle, C, is twice the radius times π:

We have in our catalog at VoxLearn.org a nice list of Web pages that describe the radius of a circle. One of them at Math Is Fun defines the radius of a circle as “the distance from the center to the edge of a circle … half the diameter.” And what do we have in this case? Exactly that: 4.5 inches.

Given the formula for the circumference above, we simply plug in the value for the radius (r) and use our calculator:

Therefore, the circumference of the circle is about 28.26 inches (I say “about” because 3.14 is not the exact value for π). Our choices are 14, 20, 28, and 63 inches, with 28 being the closest estimate.

If you thought the right answer was 14, you forgot to multiply by 2, or you thought the line itself represented the diameter of the circle, or you got confused in some other way. The answers of 20 and 63 just don’t make any sense to me. I can’t figure out how you might have gotten those answers.

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