Teacher Mechanics
Wheels Radius / Conversion of Units
Note to the teacher
On this page, students will use learn about the relationships between wheel radius, diameter, circumference, revolutions
and distance. They will also convert measurement units and use fractions and percentages. Students will use formulas
relating the measurements to compute radius, distance, or wheel revolutions when given the other 2, and in some cases
will convert units between the English and the metric systems. They will also have to find fractions or percentages of their
results. Students will have to use fractions, decimals and percentages 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, decimals and percentages, 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 3 and Wheels 4 exercises. In addition to the skills
necessary for these pages, students will also be required to multiply by fractions and percentages to calculate answers.
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.
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©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Radius / Conversion of Units
Instructions
Robot A and Robot B are being field tested.
Use the formulas below to determine the answers from the information provided.
Radius
1
1.5625”
Diameter
x
3.125”
x
Circumference
3
9.82”
3.14
3.125”
=
π (pi)
Diameter
2
2
1
4
1
Circumference
=
Revolutions
x
Inch
9.82”
Distance
=
9.82”
3. Robot A travels 17 /8 wheel revolutions and has a wheel diameter of 2.25 centimeters. Robot B travels
17 /8 wheel revolutions and has a wheel diameter 15 /16 as large.
– What is the wheel radius of Robot B in inches?
– What distance does Robot B travel in centimeters?
– What distance does Robot A travel in inches?
– What fraction of Robot A’s distance does Robot B travel?
©2005 Robomatter Inc. RE 2.5_RW 1.1
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Centimeters
=
2.54
Teacher Mechanics
Wheels Radius / Conversion of Units
After reading the instructions, students are expected to use the following procedure in the more
complex problems:
•
•
•
•
•
•
Reconstruct the equations provided as an example
Enter the data provided into these equations
Manipulate the equation if necessary
Solve the equations for the missing variable(s)
Multiply the result by a fraction or decimal
Convert measurement units if necessary
Approximate classroom time: 15-25 minutes depending on students’ background
Students successfully completing the worksheet will be able to:
1. Describe the geometry of a circle
2. Describe the relationship between radius, diameter, circumference, revolutions and distance for a wheel
3. Calculate diameter from radius
4. Calculate circumference from diameter
5. Calculate distance from wheel circumference and revolutions
6. Multiply decimals, fractions and percentages
7. Reconstruct equations relating diameter, circumference, revolutions and distance
8. Identify data provided in word problems
9. Manipulate these equations to solve for different variables
10. 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.
5.39
©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Radius / Conversion of Units
Instructions
Robot A and Robot B are being field tested.
Use the formulas below to determine the answers from the information provided.
Radius
1
1.5625”
Diameter
x
3.125”
x
9.82”
3.14
x
1
3.125”
4
1
Centimeters
=
Circumference
=
Revolutions
Circumference
3
=
π (pi)
Diameter
2
2
Inch
9.82”
Distance
=
9.82”
1. Robot A has a wheel radius of .875 inches. Robot B has a wheel 5 /8 as large.
What is the diameter of Robot B’s wheel in centimeters?
This is a three step solution. First we’ll find Robot B’s wheel radius, in inches; then we’ll find Robot B’s wheel
diameter, in inches; and finally we’ll convert the answer from inches to centimeters.
The decimal corresponding to the fraction 5 /8 is .625, so to find the radius of Robot B, we’ll just multiply
Robot A’s wheel radius by .625. .875" x .625 = .55".
Since the diameter is twice the radius, the Robot B’s wheel diameter is .55' x 2 or 1.1 inches.
Finally, we need to convert the answer from inches to centimeters. We do this by multiplying our diameter, in
inches, by 2.54 cm/inch. The final answer is 1.1" x 2.54 cm/inch = 2.79 cm.
©2005 Robomatter Inc. RE 2.5_RW 1.1
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2.54
Teacher Mechanics
Wheels Radius / Conversion of Units
2. Robot A has a wheel diameter of 3.25 centimeters. Robot B has a wheel diameter 125% as large.
What is the wheel radius of Robot B in inches?
This is also a three part problem. In part one, we’ll calculate the Robot B’s wheel diameter; in part two, we’ll
calculate its radius and in part three, we’ll convert the answer from centimeters to inches. Since Robot B’s
wheel diameter is 125% as large as Robot A’s, we have to multiply Robot A’s diameter by 1.25. Robot B’s
diameter = 3.25 cm x 1.25 = 4.06 cm.
We know that the Radius is ½ of the diameter, so Robot B’s wheel radius is ½ x 4.06 cm = 2.03 cm.
Now we’ll simply convert the radius from centimeters to inches by dividing by the conversion factor of 2.54
cm/inch: radius = 2.03 cm ÷ 2.54 cm/inch = .80 inches.
3. Robot A travels 17 /8 wheel revolutions and has a wheel diameter of 2.25 centimeters. Robot B travels 17 /8
wheel revolutions and has a wheel diameter 15 /16 as large.
– What is the wheel radius of Robot B in inches?
Since Robot B’s wheel has a diameter 15 /16 as large as Robot A, all we have to do is multiply this ratio by the
size of Robot A’s wheel. We’ll first convert the ratio from a fraction to a decimal and then multiply it by Robot
A’s wheel diameter. The fraction 15 /16 is equivalent to a decimal of .94.
When we multiply the diameter of Robot A’s wheels by this decimal, we’ll find the diameter of Robot B’s
wheel; so Robot B’s wheel diameter = 2.25 cm x .94 = 2.11 cm.
The radius is ½ the diameter, so the radius of Robot B’s wheel is 2.11 cm x ½ or 1.06 cm. To convert this to
inches, we only have to divide this answer by the conversion factor of 2.54 cm/inch; then wheel B’s
radius = 1.06 cm ÷ 2.54 cm/inch = .42 inches.
– What distance does Robot B travel in centimeters?
We just found that Robot B has a wheel diameter of 2.11 centimeters. If we find the circumference, we’ll know
how far the robot moved in one revolution. Since C = π x D, Robot B’s circumference = 2.11 cm x 3.14 =
6.63 cm. Since the robot traveled 1 7 /8 wheel revolutions, we’ll convert the wheel revolutions to a decimal
(1 7 /8 = 1.875) and multiply it by the circumference. So, distance traveled = 1.875 x 6.63 cm = 12.43 cm.
– What distance does Robot A travel in inches?
Robot A has a wheel diameter of 2.25 cm, so it has a circumference equal to π x D or 3.14 x 2.25 cm = 7.06
cm. This is the distance the robot moves in one revolution, but our robot went 1 7 /8 (or 1.875) revolutions. To
find the distance our robot traveled, multiply the distance traveled in one revolution by the number of revolutions.
Distance = 7.06 cm x 1.875 = 13.24 cm. But we want to know how far it went in inches, so we’ll just divide this
answer by the conversion factor of 2.54 cm/inch: distance = 13.24 cm ÷ 2.54 cm/inch = 5.21 inches.
– What fraction of Robot A’s distance does Robot B travel?
This is the easiest of all. Since both robots made the same number of wheel revolutions, the ratio of the
distances traveled will be the same as the ratio of their circumferences. Since the ratio of their circumferences
is the same as the ratio of their diameters, the ratio of the their distance traveled will be 15 /16 .
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©2005 Robomatter Inc. RE 2.5_RW 1.1