Andrew K. answered • 02/28/16

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Hi, Sara,

Each time the wheel rotates once around, it has traveled the distance of its CIRCUMFERENCE - the length around the outside of the circle. So, what we really need to know for this question is the circumference of the wheel. Fortunately, the circumference and diameter of a circle are always related to each other. The ratio of a circle's circumference to its diameter is always equal to π (pi).

Circumference = pi

diameter

Pi is an irrational number, usually abbreviated to 3.14. We can re-arrange this equation to solve for the circumference of this circle, since we know its diameter:

Circumference = (pi) x (diameter)

Circumference = (3.14) x (18 inches)

Circumference = 56.5 inches (rounded)

Now, since we know how far the wheel travels for each rotation, we can use unit conversion to calculate how many rotations take place per 500 miles:

500 miles x (63360 inches) x (1 rotation)

mile 56.5 inches

500 miles x (63360 inches) x (1 rotation)

mile 56.5 inches

mile 56.5 inches

= 560708 (rounded to the nearest digit) rotations every 500 miles

I hope this helps!

Andy