If a wheel has a radius of 5cm

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We can simplify the wheel, thinking of it as a simple circle, then using general knowledge about circles, we can solve this.

1) Remember that one rotation of the wheel will be equal to the perimeter of the wheel, and for a circle of radius R, the perimeter is:

$P = 2*3.14*R$

We know that our wheel has a radius of 5cm, then R = 5cm, we will get:

$P = 2*3.14*5cm =31.4 cm$

Then one full rotation of the wheel is equal to

2) Not that we know the distance that the wheel does in one single rotation, the total number of rotations needed to do a distance of 50km is equal to the quotient between 50km and the distance that the wheel moves in one rotation.

But first we need to have both values in the same unit system.

Knowin that:

1km = 1000m

1km = 100*1000cm = 100,000 cm

Then 50km = 50*(100,000 cm) = 5,000,000 cm

Now we can solve the quotient:

$\frac{5,000,000cm}{31.4cm} = 159,235.7$