SME
Grade 10 Math · Problem type
Population density
Use this for “45,000 people live within 3 km of a town’s center. How many people per km²?”
Diagram
Modeled as a circle of radius 3 km
A = π × 3² = 28.2743 km²
D
=
N
A
=
45,000
28.2743
=
1,592
people
per
km²
Each dot is 1,000 people
This is an example. Type your own values to start a new problem.
A (km²)
=
π
×
r
2
D (people per km²)
=
N (people)
÷
A (km²)
Formulas
A
=
π
×
r
2
28.2743
=
π
×
3
2
D
=
N
A
1,592
=
45,000
28.2743
Assumptions
•
Population density is people per unit of area: D = N ÷ A.
•
Model the region as a shape you know: here a circle around the center, A = πr².
•
D is an average over the whole region; some parts are more crowded than others.
Step-by-step
WE KNOW
r = 3 km, N = 45,000 people
FIND
area (A), population density (D)
Step 1 · Find area (A)
Use A = π × r²
The area of a circle is πr².
A
=
π
×
3
2
A
=
9
×
π
A
=
28.2743
km²
Step 2 · Find population density (D)
Use D = N ÷ A
Share the people out over each square kilometer.
D
=
45,000
28.2743
D
=
1,592
people
per
km²
(about
1,592
people
per
km²)
Check
Put the numbers back in. Both sides should match.
28.2743
≈
π
×
3
2
✓
1,592
≈
45,000
28.2743
✓
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