Question

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 35 minutes?

Answer 1

The tip of the minute hand of Big Ben travel in 35 minutes by 51.31 ft

Step-by-step explanation:

Angle rotated by minute hand in 1 hour = 360⁰

Angle rotated by minute hand in 60 minutes = 360⁰

Angle rotated by minute hand in 1 minute = 6⁰

Angle rotated by minute hand in 35 minutes = 35 x 6 = 210⁰

Perimeter of 1 full circle = 2πr

Perimeter of 360⁰ circle = 2πr

`\texttt{Perimeter of }210^0 \texttt{ arc =}2\pi r* (210)/(360)`

Here r = 14 feet

Substituting

`\texttt{Perimeter of }210^0 \texttt{ arc =}2\pi * 14* (210)/(360)=51.31ft`

The tip of the minute hand of Big Ben travel in 35 minutes by 51.31 ft

Answer 2

Think of the clock's face as a circle. You've been given the length of the minute hand: that tells you the radius of the circle. Use that to work out its circumference (I'm sure you already know the formula for that), then - as 35 minutes is seven-twelfths of 60 minutes - work out what seven-twelfths of that circumference is.