Question

The tires of a tractor are 4.5 feet tall. How many 360-degree rotations do the tires make when the tractor travels 170 feet? Round your answer to the nearest whole number.

Answer 1

Hello! 

Ok so we have a tire 4.5ft in diameter. We want to know how many revolutions it makes in 170ft

So we have s=r*theta where s is arc length or distance traveled and r is the radius and theta is the angle in radians that it travels through, and this is what we want to know. We are given the rest so we have;

170ft=4.5ft/2 * theta so solving for theta we get 

theta=340ft/4.5ft = 75.56 radians so now we just convert radians to revolutions and we know pi=3.14rad and 2pi is one rev and to convert to degrees its radians*( 360/2pi)=deg and this reduces to 180/pi so we have;


75.56radians * 180/pi = 4329 degrees travelled through so to get revolutions we now just divide this by 360deg for total revs. So we have;

4329deg/360deg=12 revolutions

Hope this helps! Any questions please ask! Thank you so much!