Find the area of a sector of a circle having radius r and central...

Question

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            r =  12.7 cm, θ = 81°

Accepted Answer

Hello, everyone. We are given the radius and central angle of the sector of a circle and asked to calculate the area of the sector. We want to write our answer in one decimal place. The radius is 14.9 centimeters with a central angle theta of 63 degrees. Our answer choices are a 122.1 centimeters squared. B 244.2 centimeters squared. C 81.4 centimeters squared, the 6993.3 centimeters squared. The first thing I want to do is change the from degrees to radiance cause that's what our area formula is gonna need. So 63 degrees, we want to find out what is that in radiance. So we can do this by doing 63 multiplied by pi divided by 180 and we'll have 63 pi divided by 180 and this looks like it can be reduced. Um The numerator and denominator can be reduced by nine leaving us with seven pi divided by 20. And that's gonna be our central angle theta in radiance. Now that we know that we can work with our area formula. The area of a sector is area equals one half radius squared multiplied by the central angle theta. So we know our radius is 14.9 centimeters. We found theta is seven pi divided by 20. So we're going to put this into the formula. So area equals one half multiplied by 14.9 squared, multiplied by seven pi divided by 20. Since we want this answer to be in decimal form. At this step, I'm gonna put this information into a calculator so I can get a decimal answer. And when I do that, I get 122.0564. Since we want this rounded to one decimal place, I'm going to round it to 122.1. And we know we're working with centimeters and area has square units. So our area is 122.1 centimeters squared, which is answer choice. A have a nice day.

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 12.7 cm, θ = 81°

Key Concepts

Area of a Sector

Central Angle

Units of Measurement

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