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 =  30.0 ft, θ = π/2 radians

Accepted Answer

Hello, everyone. We are given the radius and central angle of a 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 24.0 centimeters. The central angle theta is pi divided by three radians. Our answer choices are a 603.2 centimeters squared. B 301.6 centimeters squared. C 192.0 centimeters squared. D 96.0 centimeters squared. Since our central angle is already in radiance, I'm going to start by writing my formula for the area of the sector of a circle and that's the area A equals one half radius squared multiplied by theta. So theta, our central angle was pi divided by three radiance and our radius was 24.0 centimeters. So I'm gonna place those values into my formula. So I get a equals one half multiplied by 24.0 squared, multiplied by pi divided by three. Since I want my answer to be a decimal, I'm gonna use a calculator at this step to see what the decimal I get is, and I end up with 301.593. Our question wants it rounded to one decimal place. So I'm gonna round this to 301.6. We know we're working with centimeters and that area is always a square unit. So our area of that sector is 301.6 centimeters squared, which is answer choice B have a nice day.

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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 = 30.0 ft, θ = π/2 radians