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Caroline has a rock stuck in her Jeep's tire. If the tire has a 48-inch diameter, how far does the rock travel in 94° of rotation? A. 188 pi over 15 B. 47 pi over 90 C. 24π D. 47π

2 Answers

4 votes
So the problem ask to calculate the arc length of the tire if the rock is located at the 94 degree of the rotation and its diameter is 48 inches so the possible answer base on my calculation is letter A. 188 pi over 15. I hope you are satisfied with my answer and feel free to ask for more 
User Vedmant
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4 votes

Answer:

Option A


188 pi over
15

Explanation:

Step 1

Find the circumference of the tire


C=\pi D

where

D is the diameter of the tire

In this problem we have


D=48\ in

substitute the value


C=\pi (48)


C=48\pi\ in

Remember that


360\° subtends the complete circle the arc length
48\pi\ in

so

by proportion

Find how far does the rock travel in
94\° of rotation


(48\pi )/(360)=(x)/(94)\\ \\x=94*48\pi /360\\ \\x=(4,512)/(360)\pi

Simplify


x=(188)/(15)\pi

User Timothyjc
by
6.5k points