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:

$360\div 32\pi = x \div 48$

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

$x = \dfrac{360\cdot 48}{32\pi} = \dfrac{17280}{32\pi} = 171.887338539\ldots \approx 171.9$