The town of Manchester (population 50,000) has the shape of a rectangle that is 5 miles wide and 7 miles long.
Part A
What is the population density, in people per square mile, in Manchester? Round your answer to the nearest whole number of
people per square mile.
Part B
The town of Manchester contains a business area in the center of town that has the shape of a disk with the radius of 1 mile. If no
one resides in the business area, what is the population density in Manchester, in people per square mile, outside of the business
area? Round your answer to the nearest whole number of people per square mile.

Population density is expressed as the ratio of the total number of people, N living in or occupying an area or space to the total area or space. Therefore

Population density = number of people/area

A) The town of Manchester (population 50,000) has the shape of a rectangle that is 5 miles wide and 7 miles long. The area would be

5 × 7 = 35 square miles

Population density = 50000/35

= 1429 people/square mile

B) The business area has radius of 1 mile. Its area would be

πr² = 3.14 × 1² = 3.14 square miles.

The area where people reside outside the business area is

35 - 3.14 = 31.86 square miles

Population density = 50000/31.86

= 1569 people per square mile