How many complete revolutions will a bicycle wheel with a radius of 28cm make in a journey of 3 km?

Answer 1

The number of revolutions will be equal to the distance of the trip divided by the circumference of the wheel. We're already given the trip distance, and the circumference can be worked out from the radius we're given. Recall: the circumference of a circle is equal to pi multiplied by twice it's radius; or more formally:

c = 2Ï€r

In this case, r is equal to 28cm, so we can say:

c = 2Ï€28cm

≈ 2 × 3.14159265 × 28cm

≈ 175.929cm

Now we can take the distance of the trip, 3km, and divide it by the circumference of the wheel, 175.929 centimeters. That will give us the number of revolutions for the wheel:

R ≈ 3km / 175.929cm

We will of course have to convert the units first. There are one hundred thousand centimeters in a kilometer, so we can say:

R ≈ 300000cm / 175.929cm

∴ R ≈ 1705.232

That gives us the number of revolutions that would be required, but the question asks how many complete revolutions are needed. This means the last 0.232 revolutions would not be part of our final answer. Instead we can say:

R = 1705

So the wheel must do one thousand, seven hundred and five complete revolutions for a three kilometer journey.