Question

The diameter of a bicycle wheel is 2 feet.About how many revolutions does the wheel make to travel 2 kilometers?Explain.Hint 1 km =3280ft.

Answer 1

Imagine coating your front wheel in paint, then pushing it just enough forward for the wheel to go all the way around. How long is that line of paint going to be? When all's said and done, it should be just as long as the wheel's circumference. One full revolution of your bicycle's wheel moves you one circumference forward. When the question asks "how many revolutions does the wheel make to travel 2 kilometers," what it's really asking is "how many circumferences can fit in 2 kilometers?".

Before we find, that, we'll need to find what the circumference is in the first place. π, the circle constant, is defined as the ratio between the circumference of a circle and that circle's diameter. Put more compactly, π = c/d. In our case, d = 2 ft, so we can substitute that in to find that π = c/2, or c = 2π ft.

Dividing the total distance 3280 ft by 2π ft, we find that there our wheel makes exactly 3280/2π = 1640/π revolutions, or, using 3.14 as an approximation for π, approximately 1640/3.14 ≈ 522 revolutions.