To find the length of the arc created by a central angle in a circle, you can use the formula:
\[ \text{Arc Length} = r \times \theta \]
where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.
Given:
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The diameter of the circle is 30 inches, so the radius \(r\) is: \[ r = \frac{30}{2} = 15 \text{ inches} \]
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The central angle is \(7\pi/4\) radians.
Now, we can substitute the values into the arc length formula:
\[ \text{Arc Length} = 15 \times \frac{7\pi}{4} \]
We can calculate this step by step:
- Calculate \(15 \times 7 = 105\).
- Then divide by 4: \[ \frac{105\pi}{4} \]
- To approximate it numerically, use \(\pi \approx 3.14\): \[ \frac{105 \times 3.14}{4} \approx \frac{329.7}{4} \approx 82.425 \text{ inches} \]
Therefore, the length of the arc is approximately 82.5 inches.
So the answer is 82.5 in.