Chapter 10 - NCPN

Math Labs
Activity 1: The Circle of Your City
Problem Statement
A circle of latitude is the circle that is formed
by a two-dimensional plane parallel to the
equator intersecting a point of latitude. The
equation used to calculate the circle’s radius
is r = Rcos θ where r is the length of the
radius of the circle of latitude, R is the length
of the radius of Earth (3,960 miles) and θ
is the latitude in degrees. Find the radius
of the circle of latitude for any city given
the city’s latitude, and explain how a city’s
temperature relates to its latitude.
Equipment
Computer with
Internet
access
Scientific
calculator
Procedure
1 Choose any city in the world. Find a website where you can
determine the city’s latitude. sample answer: Jacksonville, FL;
latitude = 30° 19’ 55”
2 If the latitude has minutes and seconds, then convert it to a
decimal. Round your answer to the nearest hundredth.
sample answer: latitude = 30.33°
3 Find the length of the radius, to the nearest tenth, of the circle
of latitude for your city. sample answer: r = 3,418.0 miles
4 Choose another city in the opposite hemisphere and repeat
Steps 1 through 3. sample answer: Punta Arenas, Chile; r = 2,030.7 miles
5 Choose a city located on the equator. Without using the
equation, find the length of the radius of the circle of latitude.
Verify your answer using the equation. For any city on the equator,
r = 3,960 miles.
6 Draw a circle to represent the Earth. Mark the equator with
its radius. see margin
7 Use an arc to represent the circle of latitude for each of your
chosen cities. Label the radius of each. see margin
8 Write a general statement about the radius of a circle of
latitude and how it relates to the temperature of a city.
see margin
Math Labs 491