Question

Billy likes to go cycling. His bike has wheels of diameter 85 cm. He has a counter on his bike which counts the number of revolutions the wheels make. One day the counter shows 130 revolutions. How far has Billy cycled? Give your answer to the nearest metre. m​

Answer 1

347 meters

Explanation:

To calculate the distance Billy has cycled, we need to find the circumference of his bike's wheels and multiply it by the number of revolutions.

The circumference of a circle can be found using the formula: C = πd, where C is the circumference and d is the diameter of the circle.

Given that the diameter of Billy's bike wheels is 85 cm, we can find the circumference:

C = πd

C = π * 85 cm

C ≈ 267.2036 cm

Now, to find the distance Billy has cycled, we multiply the circumference by the number of revolutions:

Distance = C * number of revolutions

Distance = 267.2036 cm * 130 revolutions

Distance ≈ 34716.468 cm

Converting the distance to meters:

Distance ≈ 347.16468 meters

Therefore, Billy has cycled approximately 347 meters.

Answer 2

Explanation:

Consider this example first: Suppose the circumference of your bike tire is a nice easy number like 3ft.

If you're riding your tire and it rotates once, how far have you gone? 3ft

If it rotates twice, how far have you gone? 6ft

If it rotates four times, how far have you gone? 12ft

What if it rotates ten times?

Or 57 times?

How are you figuring this out?

You're multiplying the circumference by the number of revolutions.

In this problem, you know your tires make 150 revolutions. To find out how far it has gone, you need to know their circumference.

If you are given the diameter of the circle, the circumference is always going to be π times that diameter.

They tell you that the diameter of your tire is 85 cm. This means that the circumference of your tire must be 85π cm.

To find out how far you've traveled in cm, multiply this by the number of revolutions:

150 x 85π cm = 12750π cm

There are 100 cm in a meter, so divide this number by 100 to get the same distance in meters:

127.5π m