Question

The tip of a windshield wiper travels a distance of 31 inches in one 90 revolution. What is the

length of the windshield wiper to the nearest inch?
F 10 in.
G 15 in.
H 20 in.
J 39 in.
PLEASE HELP!!1

Answer 1

Option F, 10 inches.

Explanation:

For a circle of radius R, the perimeter is:

P = 2*pi*R

such that pi = 3.14

If we have a section of that circle defined by an angle θ, the length of the arc is:

A = (θ/360°)*P = (θ/360°)* 2*pi*R

In this case, we have a circle whose radius is defined by the length of the windshield wiper.

We also know that in one 90° revolution (so it travels the length of the arc of 90° two times) the tip travels a distance of 31 in.

Then:

A = 2*[(90°/360°)*2*3.14*R] = 31in

We need to solve this for R.

R = 31in/( 2*(90°/360°)*2*3.14) = 9.8in

We can round this to the next whole number:

R = 10in

The correct option is F.