math question?

Question

What is the outside diameter (to the nearest meter) of a circular track 6m wide if one fourth of the inside circumference is 100m?

show work.

Answer 1

You've basically got two circles here with the same center: one on the outside of the track, and one on the inside of the track. If the inside circumference is 100m, then the distance between the center of the track area and the inside edge of the track would be the inner circle's radius. Since circumference is 2pi*r, the radius is 100/(2pi), or 50/pi.

The radius of the outer circle is simply the radius of the inner circle plus the width of the actual track. So that radus is 6 + 50/pi. Using the circumference formula, the circumference of the outside track must be 2pi(6 + 50/pi) = 12pi + 100. Calulate this out and round to the nearest whole number.

Answer 2

ok - if 1/4 of the inside circumference of the circle is 100M, and circumference is pi times the diameter of the circle, then 1/4(pi)(d) = 100. pi = 3.14, figure out what d is. That's the diameter of the inside circle. Now add 6 to it (to accomodate the width of the track).

Answer 3

1/4 of the inside circumference c = 100m

(1/4)c = 100
c = 400

Outside circumference
C = c + 2π∆r = 400 + 2π6 = 400 + 12π


Outside diameter
D = C/π = (400 + 12π)/π = 400/π +12 m ≈ 139m