Questions: Estimate the length of wire to the nearest inch. Suppose that it is coiled 11 times.

Estimate the length of wire to the nearest inch. Suppose that it is coiled 11 times.
Transcript text: Estimate the length of wire to the nearest inch. Suppose that it is coiled 11 times.
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Solution

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Solution Steps

Step 1: Determine the Diameter of the Coil

The diameter of the coil is given as 18 inches.

Step 2: Calculate the Circumference of One Coil

The circumference \( C \) of a circle is calculated using the formula: \[ C = \pi \times \text{diameter} \] \[ C = \pi \times 18 \] \[ C \approx 3.14 \times 18 \] \[ C \approx 56.52 \text{ inches} \]

Step 3: Multiply the Circumference by the Number of Coils

The wire is coiled 11 times, so the total length \( L \) of the wire is: \[ L = 56.52 \times 11 \] \[ L \approx 621.72 \text{ inches} \]

Final Answer

The length of the wire to the nearest inch is approximately 622 inches.

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