CONCEPT PREVIEW Find the area of each sector.

Question

Accepted Answer

Hello, everyone. We are asked to determine the area of the indicated sector of the following circle. We are given a circle with an arc length of five pi and a radius of 20. We do not know what the angle theta is. We have answer choices. A five pi divided by two square units. B pi divided by four square units, C five pi square units D 100 pi square units. So first, I want to find the value of the. So knowing that the arc length is five pi and that's s and that the radius is 20 I can use the formula S equals are multiplied by theta. So plugging that in I get five P equals 20 multiplied by the angle theta. So I want to solve by dividing both sides by 20. And when I reduce theta will be pi divided by four. So that's our angle measure pi divided by four. So now we need to find the area, the area of a sector of a circle has a formula A equals one half radius squared multiplied by theta. So using the values we know we know A is one half multiplied by our radius of 20 squared multiplied by theta which is pi divided by four. So I'm gonna do 20 squared. So one half multiplied by 400 now multiplied by pi divided by four. And I think the easiest way to simplify this for me is to multiply straight across my num readers and then my denominator. So I will end up with a numerator of 400 pi and a denominator of eight. So now reducing this eight goes into 450 times pi does not get canceled out. So 50 pi is our answer. And since we don't know the units, we need to put it in as square units. So the area of this sector is 50 pi square units which is answer choice C have a nice day.

CONCEPT PREVIEW Find the area of each sector.

Key Concepts

Definition of a Sector

Formula for the Area of a Sector

Conversion Between Radians and Degrees

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