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Question

The wheel of a car has an outer radius of 25 cm. Calculate: a) how far the car has travelled after one complete turn of the wheel, b) how many times the wheel turns for a journey of 1 km.

Solution

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a)

Distance travelled after one complete turn of the wheel is the circumference of the wheel $C$ which is given by:

$C=2 \pi r$

Replace $r$ with $25$

$C=2 \pi \times 25=\color{#4257b2}157\ \text{cm}$

b)

The number of wheel turns is the quotient of the total distance travelled and the distance travelled after one complete turn of the wheel

For a journey of 1 $\mathrm{km}$, convert from km to cm by multiplying by 100000

Number of turns is

$\frac{100000}{157}=636.94 \approx \color{#4257b2}637\ \text{turns}$

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