Sector circle Test OG

The problem asks for the "length" - are you asking for the perimeter of the quarter circle?

I see. You might want to be cautious about using this source. If you typed the question in exactly as you found it, the question is too ambiguous to be a valid test question. It's best to study either from OG questions or from sources that spend the time and money to write questions that closely mimic the real test.

Anyway, you have three pieces to the perimeter: two radii (that's the plural of radius) and the quarter-circle arc. The radius is 100. The perimeter of the entire circle (if we had a full circle) would be 2*pi*r, or 200*pi. The arc of a quarter circle represents just one quarter of the total circumference, so (1/4) * (200pi) = 50pi.

The total perimeter of this shape, then, is 100 + 100 + 50pi, or approximately 357.

Which brings me to another reason this is not a valid test question: the test does not permit calculators, so on problems that use pi, you are not required to multiply by 3.14 - the answer choices just use pi. On the test, the correct answer choice would read "200 + 50pi" for a problem like this one. (Of course, they would use the actual symbol, not the word "pi.")

It's important to note this because, if you don't know how to get the correct answer, then you will want to examine the answer choices to see if you can find a way to eliminate wrong answers. And if you are studying answer choices that are not presented in the way they will be on the real test, then you won't be studying in an effective way.