Question

Imagine you are planning to use circles to visually compare the populations of California (38,800,000), Texas (28,240,245), and New York (19,807,500). The size of each population will be represented by the area of each circle, not the radius. Round each answer to the nearest tenth. If the circle for New York will have a radius of 5 cm, what would be the size (area) of that circle (which represents the population of New York)?What should the area and radius be for the circle representing the population of Texas?What should the area and radius be for the circle representing the population of California?

Answer 1

We will assume that there is a proportionality ratio between the area of circle and the population it represents

Part (a):
area of the circle can be calculated using the following rule:
area of circle = pi * (radius)^2
We are given that the radius for the circle representing New York is 5 cm = 0.05 meters , therefore:
area of circle representing New York = pi * (0.05)^2 = 7.85*10^-3 m^2

Part (b):
From part a, we can conclude that a circle of area = 7.85*10^-3 m^2 is used to represent a population of 19,807,500.
Therefore, we can use cross multiplication to get the area of the circle representing a population of 28,240,245 as follows:
7.85*10^-3 m^2 ................> 19,807,500
??? ...................................> 28,240,245
area of circle for Texas population = (28,240,245*7.85*10^-3)/19,807,500
area of circle for Texas population = 11.192*10^-3 m^2
area of circle = pi * radius^2
11.192*10^-3 = 3.14 * radius^2
radius^2 = 3.56433 * 10^-3
radius of circle for Texas = 0.0597 m

Part (c):
From part a, we can conclude that a circle of area = 7.85*10^-3 m^2 is used to represent a population of 19,807,500.
Therefore, we can use cross multiplication to get the area of the circle representing a population of 38,800,000 as follows:
7.85*10^-3 m^2 ................> 19,807,500
??? ...................................> 38,800,000
area of circle for California population = (38,800,000*7.85*10^-3)/19,807,500
area of circle for California population = 15.377*10^-3 m^2
area of circle = pi * radius^2
15.377*10^-3 = 3.14 * radius^2
radius^2 = 4.897 * 10^-3
radius of circle for Texas = 0.06997 m

Hope this helps :)