Circumference and Rotation Worksheet

NAME: ______Period: ______

Directions: Answer the problems below using the appropriate values and formula.

1. What is the circumference of a wheel with diameter of 4cm?

2. What is the circumference of a wheel with radius of 2cm?

3. Why are the answers for questions one and two the same when the input values are different?

The diameter is the product of twice the radius. Ergo, we can say that the diameter is twice the radius and the radius is half the diameter.

4. In questions one and two, one rotation would then be equal to what length?

*The value above can be interpreted to mean that in one rotation a wheel will travel that distance.*

5. Using the value you calculated in question four, complete the following chart:

Circumference (cm) / Rotations / Total Distance Traveled (cm)
/ 2 / 25.12cm
/ 5 / 62.8cm
/ 7 / 87.92cm
/ 10 / 125.6cm
/ 20 / 251.2cm

6. Complete the following statement: “The total distance traveled is the PRODUCTof a wheel’s circumference and the number of rotations it makes.”

7. Create a formula you can use to calculate the total distance traveled.

C = circumferenceR = rotations TD = total distance

Now, use the same formula above but, instead of C, use the variables and constants that make up C.

8. Answer the following questions using your formula:

8a. A bicycle with 24 inch diameter tires makes 100 rotations. How far did it travel?

7536 inches

8b. A Frisbee® is rolled on the ground (the person tossing it is realllllly bad at Frisbee®) and it makes 36 rotations before it is picked up. How far did it travel if the diameter of a Frisbee® is 10 inches? 1130.4 inches

8c. A monster truck traveled 207,240 inches in 1000 rotations. What is the circumference of the monster truck tire? What is the tire’s diameter? 207.24 inches and 66 inches

8d. A model car travels on an 18 foot track set up by students. If the model car has wheels that are 3 inches in diameter, how many rotations did it take the car to travel the length of the track? Round to the nearest whole number.(p.s. Check your units in this problem!) 23 rotations

8e. The London Eye Ferris wheel has a diameter of 394 ft. (en.wikipedia.org/wiki/London_Eye). If the Ferris wheel was to separate from its base and start rolling away, how many rotations would it take to travel the two miles to London Bridge? (1 mile = 5280 feet. Round your answer to the nearest tenth)8.5 rotations