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

Answer:

36.65 ft (2 dp)

Step-by-step 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:

$\sf =\dfrac{360}{60} \times 25=150^{\circ}$

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

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

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

Given:

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

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