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Chapter 5: Problem 89

The minute hand of a clock is 8 inches long and moves from 12 to 2 o'clock. How far does the tip of the minute hand move? Express your answer in terms of \(\pi\) and then round to two decimal places.

Short Answer

Expert verified
The tip of the minute hand moves approximately 8.38 inches from 12 to 2 o'clock.

Step by step solution

01

Find the full circumference

The full circumference \(C\) of a circle with radius \(r\) is given by the formula \(C = 2\pi r\). Since the radius of the circular path that the clock hand moves along is 8 inches, the full circumference is \(C = 2\pi * 8\).
02

Calculate one-sixth of the circumference

Since the minute hand moves from 12 to 2, which is one-sixth of a full circle, therefore, we calculate a sixth of the full circumference: \(C_{16} = \frac{C}{6}\).
03

Substitute the values

Substitute the value of \(C\) from step 1 into the equation: \(C_{16} = \frac{2\pi * 8}{6}\). Simplify the equation.
04

Convert to decimal

Convert the result from step 3 to decimal form. Consider \(\pi\) to be approximately 3.14 to find the decimal equivalent.

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