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.