Questions: Find the length of an arc if the radius of the arc is 4 ft and the measure of the arc is (8 π/7) (Round answer to the nearest thousandth)

Find the length of an arc if the radius of the arc is 4 ft and the measure of the arc is (8 π/7) (Round answer to the nearest thousandth)
Transcript text: Find the length of an arc if the radius of the arc is 4 ft and the measure of the $\operatorname{arc}$ is $\frac{8 \pi}{7}$ (Round answer to the nearest thousandth)
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Solution

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Solution Steps

Step 1: Given Values

We are given the radius r=4 r = 4 ft and the angle θ=8π7 \theta = \frac{8 \pi}{7} radians.

Step 2: Arc Length Formula

The formula for the length of an arc is given by: Arc Length=r×θ \text{Arc Length} = r \times \theta

Step 3: Substitute Values

Substituting the given values into the formula: Arc Length=4×8π7 \text{Arc Length} = 4 \times \frac{8 \pi}{7}

Step 4: Calculate Arc Length

Calculating the arc length: Arc Length=32π7 \text{Arc Length} = \frac{32 \pi}{7}

Step 5: Approximate Value

To find the approximate value, we calculate: Arc Length14.361566416410483 \text{Arc Length} \approx 14.361566416410483

Step 6: Round to Nearest Thousandth

Rounding the arc length to the nearest thousandth gives: Arc Length14.362 \text{Arc Length} \approx 14.362

Final Answer

14.362\boxed{14.362}

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