QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
A sector of a circle has a diameter of 22 feet and an angle of 2pi/ 3 radius. Find the area of the sector
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Answer
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Step 1:
where $r$ is the radius of the circle and $\theta$ is the angle of the sector in radians.
The area of a sector of a circle is given by the formula:
Step 2:
r = rac{1}{2} (22 ext{ feet}) = 11 ext{ feet}
In this problem, the diameter of the circle is 22 feet, so the radius is half of that:
Step 3:
A = rac{1}{2} (11 ext{ feet})^{2} (2 rac{\pi}{3} ext{ radians})
We can substitute these values into the formula:
Step 4:
(11 ext{ feet})^{2} = 121 ext{ feet}^{2}
First, square the radius:
Step 5:
121 ext{ feet}^{2} (2 rac{\pi}{3} ext{ radians}) = 242 rac{\pi}{3} ext{ feet}^{2}
Then, multiply by the angle:
Step 6:
A = rac{1}{2} (242 rac{\pi}{3} ext{ feet}^{2}) = 121 rac{\pi}{3} ext{ feet}^{2}
Finally, multiply by the constant factor:
Final Answer
The area of the sector is 121 rac{\pi}{3} square feet.
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