Radius of Circular Track: Solve for 745m & 475°

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SUMMARY

The problem involves calculating the radius of a circular track given a distance of 745 meters and an angle of 475°. The relationship between the arc length and the angle is established using the formula C/745 = 360°/475°, where C represents the circumference of the circle. By solving for C, the circumference can be determined, which is then used to find the radius using the formula C = 2πr. The correct radius is approximately 95 meters, confirming the solution provided in the textbook.

PREREQUISITES
  • Understanding of circular geometry
  • Knowledge of the relationship between arc length and angle
  • Familiarity with the formula for circumference (C = 2πr)
  • Basic algebra for solving equations
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  • Study the relationship between arc length and central angle in circular motion
  • Learn how to derive the circumference of a circle from its radius
  • Explore problems involving circular tracks and angular displacement
  • Practice using the formula C = 2πr with various examples
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Students studying geometry, particularly those tackling problems related to circular motion and arc length, as well as educators looking for examples to illustrate these concepts.

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Homework Statement


A car travels a distance of 745 m along a circular track, and the driver finds that she has traveled through an angle of 475°. What is the radius of the track?



Homework Equations


None that I know. The only thing I know is that the track is circular


The Attempt at a Solution


I used an example in my texbook which was identical to this one except the distance was 750 m and the angle was 450.

First I :
750/4=187.5( The 4 is from the 4 different quadrants)

Then I:
187.5/2=93.75------>94m

The solution in the back of the book said that the answer was 95 m but I'm not to sure if this is the right procedure.

This is the last homework problem that I have to complete before I turn it in before midnight.
 
Last edited:
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You need to know that the length of the arc of a circle is proportional to the angle.
360° corresponds to the total circumference C of the circle. 475° angle corresponds to 745 m, so C/745=360°/475°. Calculate C. How is the circumference related to the radius?

ehild
 

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