Question

A car wheel has a radius of 16 inches. Through what angle ( to the nearest tenth of a degree ) does the wheel turn when the car rolls forward 4 feet? A. 186.9° B. 171.9° C. 176.9° D. 181.9°

Answer 1

First of all, let's convert all the measures to the same unit: 4 feet are 48 inches.

Now, as the wheel turns, there is a proportion between the angle and the distance travelled: for example, when the car moves forward a whole circumference, the angle will be 360°. Conversely, if the wheel turns 180°, then the car will move forward a distance which is half the circumference of the wheel, and so on.

Since the radius is 16 inches, the circumference will be

`C=2\pi r = 32\pi`

So, we have the following proportion:

`360/ 32\pi = x / 48`

that you can read as: "if an angle of 360 corresponds to a distance travelled of
`32\pi`, then the unknown angle x corresponds to a distance travelled of 48 inches.

Solving for x, we have

`x = (360\cdot 48)/(32\pi) = (17280)/(32\pi) = 171.887338539\ldots \approx 171.9`