SME
Grade 7 Math · Problem type
Circumference and wheels
Use this for “A 28-inch wheel turns 25 times. How far does the bike go?”
Diagram
One turn covers the circumference: π diameters, a little more than 3.
C = π × d = π × 28
= 28π in ≈ 87.96 in
This is an example. Type your own values to start a new problem.
C (in)
=
π
×
d (in)
L (in)
=
C (in)
×
n
r
Radius
worked out (not typed)
Formulas
r
=
d
÷
2
(radius
=
diameter
÷
2)
14 = 28 ÷ 2
C
=
π
×
d
(circumference
=
π
×
diameter)
28π = π × 28
L
=
C
×
n
(distance
rolled
=
circumference
×
turns)
700π = 28π × 25
Assumptions
•
One turn of a wheel rolls it one circumference along the ground.
•
The distance is the circumference times the number of turns.
•
Use the diameter of the whole wheel, tire included.
Step-by-step
WE KNOW
d = 28 in (diameter), n = 25 (turns)
FIND
radius (r), circumference (C), distance rolled (L)
Step 1 · Find radius (r)
Use r = d ÷ 2 (radius = diameter ÷ 2)
The radius is half the diameter.
r
=
28
2
r
=
14
in
Step 2 · Find circumference (C)
Use C = π × d (circumference = π × diameter)
One turn rolls one circumference: π times the diameter.
C
=
π
×
28
C
=
28π
in
(≈
87.96
in)
Step 3 · Find distance rolled (L)
Use L = C × n (distance rolled = circumference × turns)
Each turn rolls one circumference: multiply by the turns.
L
=
28π
×
25
L
=
700π
in
(≈
2,199.11
in)
Check
Put the numbers back in. Both sides should match.
14 = 28 ÷ 2 ✓
28π = π × 28 ✓
700π = 28π × 25 ✓
Topic check
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