Question Video: Finding the Distance Cycled given the Radius of the Bicycle Wheel and the Number of Revolutions Mathematics • 7th Grade

A bicycle wheel has a radius of 35 cm. How far does Alice cycle on her bicycle if the wheel revolves 250 times?

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Video Transcript

A bicycle wheel has a radius of 35 centimetres. How far does Alice cycle on her bicycle if the wheel revolves 250 times?

So, I always think it’s helpful just to sketch a very quick diagram to understand the situation first. So, Alice’s bicycle here is represented by a circle. And I were told has a radius of 35 centimetres. So, to answer this question, first of all we need to work out the circumference of the bicycle wheel and then we need to multiply it by 250, as on this journey it revolves 250 times.

So, circumference, remember, is equal to two 𝜋𝑟. So, we’ll be substituting the value of 35 in as the radius here. So, we have circumference is equal to two multiplied by 𝜋 multiplied by 35, which gives us a value of 70𝜋 for the circumference of the bicycle wheel. Now, I’m going to leave it like that for now because that’s an exact value.

Now, we need to work out the total distance travelled. So, if the wheel revolves 250 times, then we need to multiply this value by 250. So, 250 times 70𝜋, which gives us 17500𝜋. Now, I’ll work out what that is as a decimal value. So, it’s 54977.8 something centimetres. Now, given that this is a distance, and we’re talking about someone travelling on a bicycle, it perhaps makes sense to convert that to more reasonable units than centimetres. So, I’ll convert it to metres by dividing by 100. So, we have an answer of 549.7787 metres. And if I round that, perhaps to the nearest metre, then I have an answer of 550 meters, to the nearest metre.

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