SME
Grade 7 Math · Problem type
Circumference is proportional to diameter
Use this for “A circle has diameter 4. What is its circumference, and where is it on the graph?”
Chart
C = 3.1416d
The line goes through (0, 0) and (1, 3.1416).
d = 2
C = 2π
k = π
This is an example. Type your own values to start a new problem.
d
Diameter
example
C
Circumference
calculated
k
Constant of proportionality
worked out (not typed)
Formulas
C
=
π
×
d
(circumference
=
π
×
diameter)
2π = π × 2
k
=
C
÷
d
(constant
of
proportionality
=
circumference
÷
diameter)
π = 2π ÷ 2
Assumptions
•
Every circle’s circumference is π times its diameter, so C and d are proportional.
•
π is the constant of proportionality: the graph is a line through (0, 0) and (1, π).
•
π is about 3.14, so a circle is a little more than 3 diameters around.
Step-by-step
WE KNOW
d = 2 (diameter)
FIND
circumference (C), constant of proportionality (k)
Step 1 · Find circumference (C)
Use C = π × d (circumference = π × diameter)
Circumference is π times the diameter.
C
=
π
×
2
C
=
2π
(≈
6.28)
Step 2 · Find constant of proportionality (k)
Use k = C ÷ d (constant of proportionality = circumference ÷ diameter)
Circumference ÷ diameter is the same for every circle.
k
=
2π
2
k
=
π
(≈
3.14)
Check
Put the numbers back in. Both sides should match.
2π = π × 2 ✓
π = 2π ÷ 2 ✓
Topic check
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