Question

Billy goes cycling.
His bike has wheels of diameter of 75cm.
He has a counter on his bike which counts the number of revolutions the wheels make.
One day, the counter shows 170 revolutions.
How far has Billy cycled?
Give answer to the nearest meter

Answer 1

Answer:

Approximately $401\; {\rm m}$.

Step-by-step explanation:

In this question, the goal is to find the distance travelled given the diameter of the wheel and the number of revolutions. To do so, multiply the number of revolutions by the distance travelled in each revolution. The distance travelled within each revolution is equal to the circumference of the wheel, which can be found from the diameter of the wheel.

The question requested an answer in meters. Hence, start by ensuring that all distance quantities are measured in meters:

$\displaystyle d = 75\; {\rm cm} \times \frac{1\; {\rm m}}{100\; {\rm cm}} = 0.75\; {\rm m}$.

The circumference of this wheel would be:

$C = \pi\, d = (0.75\, \pi)\; {\rm m}$.

In other words, the bike travels a distance of $0.75\, \pi$ meters after each complete revolution of the wheel. The distance travelled after $170$ revolutions would be:

$(170)\, (0.75\, \pi\; {\rm m}) \approx 401\; {\rm m}$.

(Rounded to the nearest meter.)