Chapter 6, Problem 88RE

To determine

To Calculate: Distance travelled by minute hand tip in 20 minutes and 30 minutes.

Answer to Problem 88RE

Distance travelled by minute hand in 30 minutes $25.14inch$

Distance travelled by minute hand in 30 minutes $16.76inch$

Explanation of Solution

Given information:

Length of minute hand.

Formula used:

Length of Arc $=\frac{\theta }{{360}^{°}}\times 2\pi r$

Angle swiped by minute hand in 60 minutes $={360}^{°}$

Angle swiped by minute hand in 1 minute $=\frac{{360}^{°}}{60}=6^{°}$

Angle swiped by minute hand in 30 minute $6^{°}\times 30={180}^{°}$

Distance travelled by tip of minute hand in 30 minutes:

  $\begin{array}{l}=\frac{\theta }{{360}^{°}}\times 2\pi r\\ =\frac{{180}^{°}}{{360}^{°}}\times 2\times \frac{22}{7}\times 8\\ =25.14inch\end{array}$

Distance travelled by minute hand in 30 minutes $25.14inch$

Angle swiped by minute hand in 60 minutes $={360}^{°}$

Angle swiped by minute hand in 1 minute $=\frac{{360}^{°}}{60}=6^{°}$

Angle swiped by minute hand in 20 minute $6^{°}\times 20={120}^{°}$

Distance travelled by tip of minute hand 20 minutes:

  $\begin{array}{l}=\frac{\theta }{{360}^{°}}\times 2\pi r\\ =\frac{{120}^{°}}{{360}^{°}}\times 2\times \frac{22}{7}\times 8\\ =16.76inch\end{array}$

Distance travelled by minute hand in 30 minutes $16.76inch$