Question

Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Big Ben travel in 25 minutes? Round to two decimal places.

Answer 1

36.65 ft (2 dp)

Explanation:

• Angles around a point sum to 360°
• 1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

`\sf =(360)/(60) * 25=150^(\circ)`

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

`\textsf{Arc length}=2 \pi r\left((\theta)/(360^(\circ))\right)`

`\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}`

Given:

• r = length of minute hand = 14 ft
• 
  `\theta` = 150°

`\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left((150^(\circ))/(360^(\circ))\right)\\ & = 28\pi \left((5)/(12)\right)\\ & = (35)/(3) \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}`