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