Teacher Mechanics
Wheels Diameter / Distance Word Problems
Note to the teacher
On this page, students will use word problems to learn about the relationships between wheel radius, diameter,
circumference, revolutions and distance. They will also convert measurement units. Students will use formulas relating the
measurements to compute distance, diameter or wheel revolutions when given the other 2, and in some cases will convert
units between the English and the metric systems. Students will have to use both fractions and decimals to make these
calculations, and will also have to reconstruct and manipulate equations. While the worksheet is designed to help students
learn the geometry of the circle and the relationship between wheel size, revolutions and distance, and is also designed to
provide the information needed to convert units between English and metric systems, and may be completed by students
with little background in these areas, the existing ability to multiply fractions and decimals, and the ability to manipulate
equations, will be necessary to successfully complete the worksheet. Teachers may wish to review any or all of these skills
depending on their students’ background.
Note that these exercises are more challenging than the Wheels 1 and Wheels 2 exercises. In addition to the skills
necessary to complete those pages, students will also be required to manipulate equations to solve for different variables.
Note also that there are no instructions regarding rounding. The answers assume rounding to 2 digits beyond the decimal
place, except for known fractions. Teachers may wish to supply additional instructions. If they do not, students’ answers
will vary slightly according to what rounding conventions they use.
Instructions
After testing their robot using wheels of different sizes, Katie and Ross lost some of the data they recorded.
Use the tables below to fill in the missing data described in the questions below.
π (pi)
Diameter
1
1.125"
x
3.14
Circumference
2
3.53"
Circumference
=
Distance
Revolutions
x
2
3.53"
=
7.06"
1.
1. In the first test, Ross and Katie recorded that the wheel diameter was 1.125 inches and that the robot was
programmed to move 2 wheel revolutions. How far did their robot move in inches?
2.
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©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Diameter / Distance Word Problems
After reading the instructions, students are expected to use the following procedure:
•
•
•
•
•
Reconstruct the equations provided as an example
Enter the data (1. and 2.) provided into these equations
Manipulate the equation if necessary (manipulation is not required in the example above)
Solve the equations for the missing variable(s) (3.)
Convert measurement units if necessary
Approximate classroom time: 15-30 minutes depending on students’ background
Students successfully completing the worksheet will be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Describe the geometry of a circle
Describe the relationship between radius, diameter, circumference, revolutions and distance for a wheel
Calculate circumference from diameter
Calculate distance from wheel circumference and revolutions
Multiply decimals and fractions
Reconstruct equations relating diameter, circumference, revolutions and distance
Identify data provided in word problems
Manipulate these equations to solve for different variables
Convert between English and metric measurement units
Standards addressed:
Math Standards
Numbers and Operations
Algebra
Geometry
Measurement
Problem Solving
Connections
Technology Standards
The Nature of Technology Standards 1
Design Standards 8, 9, 10
Note: Workbook answers begin on the next page.
©2005 Robomatter Inc. RE 2.5_RW 1.1
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Teacher Mechanics
Wheels Diameter / Distance Word Problems
Instructions
After testing their robot using wheels of different sizes, Katie and Ross lost some of the data they recorded.
Use the tables below to fill in the missing data described in the questions below.
π (pi)
Diameter
1
1.125"
x
Circumference
2
3.53"
3.14
Circumference
=
Distance
Revolutions
x
2
3.53"
=
7.06"
1. In the first test, Ross and Katie recorded that the wheel diameter was 1.125 inches and that the robot was
programmed to move 2 wheel revolutions. How far did their robot move in inches?
To solve this, we first have to find the circumference of the wheel since this will tell us how far the robot moved in
one wheel revolution. We know, from solving problems in previous sections of the workbook that C = π x D, so
C = 3.14 x 1.125" = 3.53" To find the total distance, we need to multiply the circumference by the number of
revolutions that the wheel makes: distance = 3.53 inches / revolution x 2 revolutions = 7.06".
2. In the second test, Ross and Katie recorded that their robot moved 8.65 inches and that the robot was
programmed to move 3.5 wheel revolutions. What was the diameter of the wheel in inches?
If we want to find the diameter of the wheel, the first thing we’ll need to do is find the circumference. We know
that the robot moved 8.65” in 3.5 revolutions. What we want to know is how far did it go in one revolution
(remember, that’s the definition of the circumference). To find the circumference, we simple divide the distance
by the number of revolutions: C = 8.65 inches/3.5 revolutions = 2.47 inches. Since we already know that
C = π x D, we can solve for D and find that D = C/ π : D = 2.47"/3.14 = .79".
3. In the third test, Ross and Katie recorded that their robot moved 5.69 inches and that the wheel diameter was 1.75
inches. How many wheel revolutions was the robot programmed to complete?
Again, we first need to find the circumference of the wheel. Since C = π x D, we can see that: C = 3.14 x 1.75" =
5.50" If we divide the total distance traveled by the circumference, we’ll be able to find the number of revolutions
the robot was programmed for: revolutions = 5.69 inches/5.50 (inches/revolution) = 1.03 revolutions .
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©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Diameter / Distance Word Problems
4. In the fourth test, Ross and Katie recorded that their robot moved 15.38 centimeters and that the robot was
programmed to move 3.5 wheel revolutions. What was the diameter in inches of the wheel they used in this
iteration? What was the diameter in centimeters?
You know the calculations are the same, whether we do it in the metric or English system. We can find the wheel
circumference by dividing the distance traveled by the number of revolutions that the wheel made. Just because
we’re asked for the wheel diameter, in centimeters, second, doesn’t mean that we have to do it second. It would
be so much easier to calculate the diameter in centimeters, first, because our measurements are already in centimeters. So the circumference is: C = 15.38 centimeters / 3.5 revolutions = 4.39 centimeters. And since
D = C/ π, from problem 2, above, we can find the diameter: D = 4.39 cm / 3.14 = 1.40 cm. As we learned
earlier, the conversion factor is 2.54 cm/inch. To find the diameter, in inches, we simply divide the diameter, in
cm, by the conversion factor: D = 1.40 cm/2.54 (cm/inch) = 0.55 inches.
5. In the fifth test, Ross and Katie recorded that the wheel diameter was 2.43 inches and that the robot was programmed
to move 1.75 wheel revolutions. How far did their robot move in inches? How far did it move in centimeters?
Remember that the circumference is equal to π times the diameter. So: C = 3.14 x 2.43" = 7.63". Since the
robot made 1.75 wheel revolutions, the total distance traveled would be: distance traveled = 7.63" x 1.75 =
13.35". To get that same distance in centimeters, all we need to do is multiply the distance, in inches, times the
conversion factor, 2.54 cm/inch: distance traveled = 13.35 inches x 2.54 cm/inch = 33.91 cm.
©2005 Robomatter Inc. RE 2.5_RW 1.1
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