Question

The diameter of the wheels on your car is 25 inches. You are going to drive 458 miles today. Each of your wheels is going to turn by an angle of ___ degrees.
Hint: a mile has 5280 feet. A foot has 12 inches, and the circumference of a circle with a diameter of d equals (pi)d

Answer 1

d = Diameter of wheels = 25 inches

s = Distance to be traveled by the wheels = 458 miles

Converting the miles to inches

$s=458\times 5280\times 12=29018880\ \text{inches}$

The distance traveled by the wheels in rotation is the circumference

$D=\pi d\\\Rightarrow D=\pi\times 25$

The number of rotations required to cover the distance would be

$\dfrac{s}{D}\\ =\dfrac{29018880}{\pi\times 25}\\ =369479.855599$

$1$ rotation is $360^{\circ}$ so

$369479.855599\times 360=133012748.016^{\circ}$

The number of rotations to cover the required distance is $133012748.016^{\circ}$

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