Question

a Wheel 15 inches in diameter is spun around 4 full turns. What distance,to the nearest inch, did a mark on the edge of the wheel travel in those four turns ? explain how you figured out your answer

Answer 1

C=π*d so the distance the mark travels in 1 revolution is 15*π. for 4 revolutions we get 60π and this is approx 189 inches

Answer 2

If the wheel has a diameter of 15 inches, its radius is half that, or 7.5 inches then.

a full turn, or a full cycle around the wheel, namely around the circle is 360° or 2π radians.

now, in one turn or cycle, it covered an angle of 2π, in 2 cycles it covered 2(2π), in 3 it did 3(2π) and in 4 of course 4(2π).

so, what is the arc's length, whose radius is 7.5 and its central angle is 8π?

well.... you already know that s = rθ, therefore then, s = (7.5) (8π).