You may recall that the perimeter of an object is the distance around the edge of the object. If the object contains circles, then you may need to think about the circumference of a circle, which is the perimeter of the circle.

 

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Problem

A tire on a passenger car has a diameter of 18 inches. When the tire has rotated 5 times, how far will the car have traveled?

car with a tire highlighted

Step 1: Read, understand, and interpret the problem.

  • What information is presented?

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    Check Your Answer

    The diameter of the tire is 18 inches.
    The tire will rotate 5 times. Close Pop Up
  • What is the problem asking me to find?

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    Check Your Answer

    The distance that a point on the tire will travel when the tire rotates 5 times.
    I will need to find the circumference of the tire. Close Pop Up
  • What information may be extra information that I do not need?

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    Check Your Answer

    There is not any extra information in the problem. Close Pop Up
Step 2: Make a plan.

  • Draw a picture
  • Use a formula: Which formula do I need to use?
    (Hint: Look at your Mathematics Reference Materials)

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    Check Your Answer

    C = Πd
    Circumference = Π × diameter Close Pop Up
Step 3: Implement your plan.

  • What formulas do I need?

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    Check Your Answer

    C = Πd
    Circumference = Π × diameter Close Pop Up
  • What information can I interpret from the diagram, table, or other given information?

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    Check Your Answer

    5 rotations will equal 5 times the circumference of the tire. Close Pop Up
  • Solve the problem.

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    Check Your Answer

    Answer: 282.6 inches
    C = Πd ≈ 3.14(18 inches) = 56.52 inches
    5 rotations = 5(C) = 5(56.52 inches) = 282.6 inches Close Pop Up
Step 4: Evaluate your answer.

  • Does my answer make sense?

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    Check Your Answer

    Yes. 56.52 inches is about 60 inches, and 5 times 60 inches is 300 inches. My answer, 282.6 inches, rounds to 300 inches, so my answer is reasonable. Close Pop Up
  • Did I answer the question that was asked?

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    Check Your Answer

    Yes. I was asked to determine the distance traveled in 5 rotations, which is 5 circumferences of the circle. Close Pop Up
  • Are my units correct?

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    Check Your Answer

    Yes. I was given information in inches, and my answer is also in inches. Close Pop Up

Practice

A cylindrical barrel with a diameter of 20 inches is used to hold fuel for a barbecue cook off. The chef rolls the barrel so that it completes 7 rotations. How many feet did the chef roll the barrel?

barrel on its side
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Hint

You need to determine the circumference of the barrel. Also, be aware that the diameter is given in inches, but the question asks for the number of feet that the barrel is rolled. You will need to convert inches to feet. Close Pop Up
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Check Your Answer

Close Pop Up