Question

A bicycle wheel has outer diameter 32cm. How far will the cyclist travel if the wheel rotates 100π times? Give your answer in kilometres and correct to two decimal places.

Answer 1

`T=0.3142km \\T=0.31km\ to\ 2dp`

Explanation:

Diameter
`d=32cm=0.32m`

Number of rotations
`N=100\pi`

Generally the circumference of the wheel is mathematically given as

`C=2\pi r`

`C=2\pi (0.32)^2/4`

`C=1.005309649m`

`C=1.0m`

Generally the total distance traveled T is mathematically given as

`T=N*C`

`T=100\pi *1m`

`T=314.1592654m \approx 314.16m`

Total distance traveled T in Kilometres

`T=314.1592654m`

`T=(314.1592654m)/(1000)`

`T=0.3142km \\T=0.31km\ to\ 2dp`