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SAT Math 8.5 Geometry and Measurement 186 Views


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SAT Math 8.5 Geometry and Measurement

Language:
English Language

Transcript

00:02

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

00:07

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

00:14

What is the approximate perimeter of the figure?

00:18

Here are the potential answers...

00:21

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

00:25

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

00:30

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

00:32

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

00:39

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

00:43

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

00:47

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

00:53

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

01:00

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

01:07

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

01:11

The formula is 2 pi r.

01:13

So, we have our “r” now,

01:16

2 pi times 12 is 24 pi.

01:19

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

01:25

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

01:30

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

01:34

…18.84 plus 12 plus 12 = 42.84…

01:39

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

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