ShmoopTube

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Incoming Shmoopy question at 5 o'clock! Everyone duck.

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The area of this figure, cut from the center of a circle, is 36π units squared.

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What is the approximate perimeter of the figure?

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Here are the potential answers...

00:21

Okay, so we have what immediately reminds us of a baseball field…

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…especially with that right angle symbol-slash-baseball diamond there in the corner.

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So we’re told that this thing is cut from the center of a circle…

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…and since we know the angle is 90 degrees, we can be sure that this is exactly one-fourth of a circle.

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We’re also told that the area is 36 pi units squared…

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…so it seems pretty clear that the area of the COMPLETE circle should be four times that amount.

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4 times 36 pi is 144 pi. The area of a circle is pi times r squared…

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so we need to take the square root of 144… which leaves us with a radius of 12.

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Cool, now we’ve got the length of each of our sides. But…what about the arc?

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For this bit we need to know the circumference, of the circle.

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The formula is 2 pi r.

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So, we have our “r” now,

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2 pi times 12 is 24 pi.

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24 pi works out to about 75.36…which is the perimeter of the entire circle.

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Divide that by 4 to get the measure of just this arc… and we get 18.84.

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We’ll have to add our two sides to that amount so we get…

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…18.84 plus 12 plus 12 = 42.84…

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…which, when rounded, is 43… answer E.

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