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)

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)

Solution

Solution Steps

Step 1: Given Values

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

Step 2: Arc Length Formula

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

Step 3: Substitute Values

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

Step 4: Calculate Arc Length

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

Step 5: Approximate Value

To find the approximate value, we calculate: \[ \text{Arc Length} \approx 14.361566416410483 \]

Step 6: Round to Nearest Thousandth

Rounding the arc length to the nearest thousandth gives: \[ \text{Arc Length} \approx 14.362 \]

Final Answer

$\boxed{14.362}$

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