The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?

Question

jim_thompson5910 · Answer

What is the circumference of this circle (radius = 11)?

anonymous · Answer

C=2(pi)r
c=2(11)pi
c-22pi

jim_thompson5910 · Answer

22pi, yes

jim_thompson5910 · Answer

so if the wiper traced out a path that was exactly 22pi inches, then it would cover the entire circle

however, it's just 31 inches, so it covers just a fraction or portion of this circumference

jim_thompson5910 · Answer

In radians, a full rotation is 2pi radians

we multiply the fraction 31/(22pi) by 2pi to get

$$\Large \frac{31}{22\pi}*2\pi = \frac{62\pi}{22\pi} = \frac{31}{11}$$

jim_thompson5910 · Answer

So that's the radian measure of the angle. Notice how if we did a full rotation we'd multiply 2pi by (22pi)/(22pi) =1 to get 2pi

which is what we should expect

anonymous · Answer

thank you so much :)