QuestionOctober 24, 2026

Find the area of a sector of a circle having radius r and central angle Theta r=60.0mi,Theta =125^circ The area is approximately square mi^2 (Do not round until the final answer. Then round to the nearest tenth as needed.)

Find the area of a sector of a circle having radius r and central angle Theta r=60.0mi,Theta =125^circ The area is approximately square mi^2 (Do not round until the final answer. Then round to the nearest tenth as needed.)
Find the area of a sector of a circle having radius r and central angle Theta r=60.0mi,Theta =125^circ The area is approximately square mi^2 (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solution
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Answer

The area is approximately \( 3927.0 \, \text{mi}^2 \) Explanation 1. Understand the formula for the area of a sector The area ( A ) of a sector of a circle with radius ( r ) and central angle ( \Theta ) (in degrees) is given by the formula: \[ A = \frac{\Theta}{360} \times \pi r^2 \] 2. Substitute the given values into the formula Substitute \( r = 60.0 \, \text{mi} \) and \( \Theta = 125^\circ \) into the formula: \[ A = \frac{125}{360} \times \pi \times (60)^2 \] 3. Calculate the area First, calculate \( \frac{125}{360} \): \[ \frac{125}{360} \approx 0.347222 \] Then calculate \( \pi \times (60)^2 \): \[ \pi \times 3600 \approx 11309.73355 \] Finally, multiply the results: \[ A \approx 0.347222 \times 11309.73355 \approx 3926.9907 \] 4. Round to the nearest tenth Round ( 3926.9907 ) to the nearest tenth: \[ A \approx 3927.0 \, \text{mi}^2 \]

Explanation

1. Understand the formula for the area of a sector<br />The area ( A ) of a sector of a circle with radius ( r ) and central angle ( \Theta ) (in degrees) is given by the formula: <br />\[ A = \frac{\Theta}{360} \times \pi r^2 \]<br /><br />2. Substitute the given values into the formula<br />Substitute \( r = 60.0 \, \text{mi} \) and \( \Theta = 125^\circ \) into the formula:<br />\[ A = \frac{125}{360} \times \pi \times (60)^2 \]<br /><br />3. Calculate the area<br />First, calculate \( \frac{125}{360} \):<br />\[ \frac{125}{360} \approx 0.347222 \]<br /><br />Then calculate \( \pi \times (60)^2 \):<br />\[ \pi \times 3600 \approx 11309.73355 \]<br /><br />Finally, multiply the results:<br />\[ A \approx 0.347222 \times 11309.73355 \approx 3926.9907 \]<br /><br />4. Round to the nearest tenth<br />Round ( 3926.9907 ) to the nearest tenth:<br />\[ A \approx 3927.0 \, \text{mi}^2 \]
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