22. (C)
The population equals ∑ (area · density). We partition the interval [0,10] along a radius
from the center of town into 5 equal subintervals each of width Δr = 2 mi. We will divide
Winnipeg into 5 rings. Each has area equal to (circumference × width), so the area is 2πrk
Δr or 4πrk. The population in the ring is
(4πrk)· (density at rk) = 4πrk · f (rk).
A Riemann sum, using left-hand values, is 4π · 0 · 50 + 4π · 2 · 45 + 4π · 4 · 40 + 4π · 6 · 30
+ 4π · 8 · 15 = 4π(90 + 160 + 180 + 120) 6912 hundred people—or about 691,200
people.
