A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?

Answer 1

arc length = radius times radians = radius times the angle measured in radians

L = 26 x 80(pi/180) = 26(8)3.14159/18 =about 36.3 inches arc length

had it been 90 degrees, the circumference would have been 1/4 of 26 x pi = 26/2 times pi = 13 x pi = 13(3.14159) = about 40.8 inches

which is about 12% (80+.12(80) = 89.6) more than 36.3. 36.3+4.36 = 40.7 = about 40.8