Chapter 12.1, Problem 19IP

a.

To determine

To find: how far the minute hand travels after given number of rotations around the clock face. Round to the nearest hundredth.

(a) 2 rotations

Answer to Problem 19IP

49.76 meters.

Explanation of Solution

Given information: The tower at Philadelphia City Hall contains four clocks that have a radius of about 3.96 meters.

Formula used:

The circumference formula is:

  $C=2\pi r$ , where r is the radius.

Calculation:

As the minute hand around the clock, the tip of the hand traces a circumference.

To find the length of one rotation by applying the circumference formula.

  $\begin{array}{l}C=2\pi r\\ r=3.96(\text{given})\\ C=2\pi \times 3.96\approx 24.88\text{meters}\text{.}\end{array}$

  $2\text{rotation}=2C=2\times 24.88=49.76\text{meters}.$

b.

To determine

To find: how far the minute hand travels after given number of rotations around the clock face. Round to the nearest hundredth.

(b) $\frac{1}{2}$ rotation

Answer to Problem 19IP

12.44 meters.

Explanation of Solution

Given information: The tower at Philadelphia City Hall contains four clocks that have a radius of about 3.96 meters.

Formula used:

The circumference formula is:

  $C=2\pi r$ , where r is the radius.

Calculation:

As the minute hand around the clock, the tip of the hand traces a circumference.

To find the length of one rotation by applying the circumference formula.

  $\begin{array}{l}C=2\pi r\\ r=3.96(\text{given})\\ C=2\pi \times 3.96\approx 24.88\text{meters}\text{.}\end{array}$

  $\frac{1}{2}\text{rotation}=\frac{1}{2}C=\frac{1}{2}\times 24.88=12.44\text{meters}.$

c.

To determine

To find: how far the minute hand travels after given number of rotations around the clock face. Round to the nearest hundredth.

(c) $5\frac{3}{4}$ rotations.

Answer to Problem 19IP

143.06 meters.

Explanation of Solution

Given information: The tower at Philadelphia City Hall contains four clocks that have a radius of about 3.96 meters.

Formula used:

The circumference formula is:

  $C=2\pi r$ , where r is the radius.

Calculation:

As the minute hand around the clock, the tip of the hand traces a circumference.

To find the length of one rotation by applying the circumference formula.

  $\begin{array}{l}C=2\pi r\\ r=3.96(\text{given})\\ C=2\pi \times 3.96\approx 24.88\text{meters}\text{.}\end{array}$

  $5\frac{3}{4}\text{rotation}=5\frac{3}{4}C=5\frac{3}{4}\times 24.88=143.06\text{meters}.$