In Exercises 75–78, find the area of the sector of a circle of...

Question

In Exercises 75–78, 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: 10 meters Central Angle, θ: θ = 18°

Accepted Answer

Hello, today we're going to be calculating the area of the sector of a circle. So we are told that we want to calculate the area of the sector of a circle with the radius of 12 m. The sector has a central angle of 24 degrees. And we want to write the answer in terms of pi and a decimal form rounded to the nearest 100th. So let's go ahead and draw an image. So we have this circle and we have a sector inside of the circle. We are told that the circle has a radius of 12 m. So the circle contains a radius of 12 m and we are told that the central angle of the sector is 24 degrees. So we have data as 24 degrees and we want to use this information to find the area inside of this sector. But we have an equation to help us do that. The equation for the area of a sector of a circle is given to us as a is equal to one half multiplied by R squared multiplied by theta. Here R represents the radius and data represents the central angle. And we already have that information. We are told that R is equal to 12 m and we are told that data is equal to 24 degrees. Now keep in mind that we want our answer to be in terms of pie, in order to get our answer, in terms of pi we'll need to convert degrees to radiance. So we'll need to multiply the by the quantity pi over 80 doing so will give us a theta of 24 pi over 1 80 which will simplify to leave us with two pi over 15. Now that we have R and we have the, if we were to plug in these quantities into the area of the sector of a circle, we are left with a s equal to one half multiplied by 12 m quantity squared multiplied by two pi over 15, 12 m squared will leave us with 144 m squared. So we have one half multiplied by 144 m squared, multiplied by two pi over 15, a half multiplied by 144 will leave us with 72. So we have 72 m squared multiplied by two pi over 15. And if we multiply these quantities together, we are left with 48 pi over m squared. So this will be the value of the area of the sector of the circle. But we also want this area to be in decimal form rounded to the nearest 100th. If we were to plug in 48 pi over five into a calculator and round to the nearest 100th, we will get an approximate value of 30. meters squared. So just to summarize we the area of the sector of the circle in terms of pi is 48 pi over five and in decimal form is approximately 30.16 m squared. With that being said, the answer to this problem is going to be D. 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.

In Exercises 75–78, 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: 10 meters Central Angle, θ: θ = 18°

Key Concepts

Area of a Sector

Central Angle in Degrees

Rounding Numerical Results

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