Find the area of the sector of a circle of radius r formed by ...

Question

Find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 4 inches Central Angle, θ: θ = 240°

Accepted Answer

Hello, today we're gonna be calculating the area of the sector of a circle. So we are told to calculate the area of a sector of a circle with the radius of 18 inches. The sector has a central angle of 185 degrees. And we want to write the answer in terms of pi and in a decimal form rounded to the nearest 100th. So let's go ahead and draw an image to help us understand what's going on. So we have this sector that is inside of a circle. We are told that we want to calculate the area of the sector. So we want the area of everything inside the sector. We are told that the circle has a radius of 18 inches and we are also told that the sector has a central angle of 185 degrees. So theta is equal to 1 85. So how do we go about solving for an area of a sector of a circle? Well, we have a formula that helps us do that. The area of the sector of a circle is given to us as a is equal to one half times radius squared times theta. So here we have our radius R is going to equal to 18 and theta is given to us as 185 degrees. Now keep in mind that the problem states that we want our answer to be in terms of pie, our data is given to us in terms of degrees. So we're going to have to convert it from degrees to radiance. In order to do that, we can multiply 1 85 by pi over 80. Doing so is going to give us the quantity of 185 pie over 180. And this fraction is going to simplify to give us pi over 36. So this is going to be the in terms of radiance. Now that we have our R and we have data in terms of radiance, we can plug this into the formula for the area of the sector to get the area of the sector of the circle. So doing so is going to give us the equation A is equal to one half times 18 squared times 37 pi over 36. And now we just need to simplify 18 squared is going to simplify to give us the value of and one half times 324 is going to give us the value of 162. So A is equal to 162 multiplied by 37 pi over 36 multiplying these two values together is going to give us 994 P over 36. And this value is going to simplify to give us pi over two. So the area of the angle or the area of the sector in terms of radiance is 333 pi over two. Now keep in mind that we want this value to also be in the form of a decimal rounded to the nearest 100th. In order to do that, you can plug in this fraction into a calculator and round the given decimal to the nearest hundreds place. And doing so should give you an approximate decimal of 523.8 inches. So this is going to be the area of the sector in the form of a decimal. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 4 inches Central Angle, θ: θ = 240°

Key Concepts

Area of a Sector

Central Angle in Degrees

Rounding and Expressing Answers

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