Question

1. justify the diameter of a wheel is 15 inches. how far would your hand move in one full turn of the wheel if you do not let go of the wheel? round the answer to the nearest inch. (use 3.14 for π.) describe how to tell whether your answer is reasonable.

Explanation:

Step1: Find the circumference formula

The formula for the circumference of a circle is \(C = \pi d\), where \(d\) is the diameter.

Step2: Substitute the values

Given \(d = 15\) inches and \(\pi=3.14\), then \(C=3.14\times15\).

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Step3: Round the result

Rounding \(47.1\) to the nearest inch gives \(47\) inches.

To check if the answer is reasonable:

• We know that \(\pi\approx3\). If we use \(\pi = 3\), then \(C=\pi d=3\times15 = 45\) inches.
• Since the actual value of \(\pi = 3.14\) (a bit larger than \(3\)), the result \(47.1\approx47\) (which is a bit larger than \(45\)) is reasonable.

Answer:

The hand would move approximately \(47\) inches.