Maths Quest A Year 11 for Queensland Chapter 6 Earth geometry WorkSHEET 6.1
1
Use the world map above for the following questions, where necessary.
1 Draw a sphere to represent the shape of the
Earth. Mark in:
(a) the prime meridian
(b) the equator
Indicate whether latitude or longitude (in degrees).
2 Indicate whether the following lines of latitude/longitude lie on great circles or small circles.
(a)
15ºN
(b)
15ºE
(c)
15ºW
(d)
15ºS
(e) 0ºS
3 A sphere has a radius of 20 cm. Calculate the length of the great circle on its surface.
(a) small circle
(b) great circle
(c) great circle
(d) small circle
(e) great circle
A great circle is the largest circle on the surface of the sphere. It is the circumference of the circle with radius ‘ r
’. length of
C great circle


2
2
 r
  
20

125.66
cm cm

Maths Quest A Year 11 for Queensland Chapter 6 Earth geometry WorkSHEET 6.1
4 A small circle on the sphere in question 3 has a length of 50 cm. What is the radius of the small circle?
C

50

2
 r
2
   r

2
50
  

7 .
96 cm
 r r
5 Use the world map to give approximate positions of the following towns.
(a) Tokyo
(b) Manila
(c) Auckland
(d) Oslo
(e) Santiago
6 Locate the city closest to each of the following locations.
(a)
20ºS, 180ºE
(b)
30ºN, 120ºE
(c) 35ºN, 120ºW
(d)
35ºS, 20ºE
(e)
40ºN, 10ºE
7 State the latitude of the following (in degrees):
(a) Tropic of Capricorn
(b) North Pole
(c) equator
(d) Tropic of Cancer
(e) South Pole
8 State the line of longitude with the following feature:
(a)
180ºW
(b)
0ºE
So, the radius of the small circle = 7.96 cm.
(a) 35ºN, 140ºE
(b)
15ºN, 120ºE
(c)
35ºS, 170ºE
(d)
60ºN, 10ºE
(e) 35ºS, 70ºW
(a) Suva
(b) Shanghai
(c) Los Angeles
(d) Cape Town
(e) Rome
(a) 23
1
2

S
(b)
90ºN
(c) 0ºN or 0ºS
(d) 23
1

2
N
(e)
90ºS
(a) International Date Line
(b) prime meridian
2
9 Draw separate spheres to pinpoint the following locations on the Earth’s surface.
(a)
Point X (20ºN, 80ºE)
(b)
Point Y (20ºS, 80ºW)

Maths Quest A Year 11 for Queensland Chapter 6 Earth geometry WorkSHEET 6.1
10 The radius of the Earth is approximately
6370 km. Calculate the length of the equator.
The equator is a great circle, so its length is measured by the circumference of the circle, the radius of which is 6370 km.
C

2
 r

2
  
6370 km

40 024 km
So, the Equator is approximately 40 000 km in length.
3