Practice Maths

Topic Review — Earth Geometry and Time Zones — Solutions

← Earth Geometry and Time Zones

This review covers latitude and longitude, great circles and small circles, distances on Earth’s surface, and time zones. Click each answer to reveal the worked solution.

Review Questions

  1. State the latitude and longitude of a point that is 25° south of the equator and 140° east of the prime meridian.
    (25°S, 140°E)
    This coordinate is approximately where Townsville, Queensland is located.
  2. Which is further from the equator: 48°N or 37°S? By how many degrees?
    48°N is further by 48 − 37 = 11 degrees.
  3. Classify each as a great circle or small circle: (a) equator   (b) 30°N parallel   (c) 0° meridian   (d) Antarctic Circle (66.5°S)
    (a) Equator: great circle
    (b) 30°N parallel: small circle
    (c) 0° meridian (with 180° together): great circle
    (d) Antarctic Circle: small circle
  4. Two cities lie on the same meridian at (15°N, 45°E) and (45°N, 45°E). Find the great circle distance between them.
    θ = 45° − 15° = 30°
    d = (π × 6400 × 30) / 180 ≈ 3 351 km
  5. Two cities are on the equator at 20°W and 100°E. Find the distance between them along the equator.
    θ = 20° + 100° = 120°
    d = (π × 6400 × 120) / 180 ≈ 13 404 km
  6. A city is at 40°N latitude. What is the radius of its parallel of latitude? What is the circumference of this small circle?
    r = 6400 × cos(40°) = 6400 × 0.7660 ≈ 4902 km
    Circumference = 2π × 4902 ≈ 30 806 km
  7. Two cities are both at 50°N, with longitudes 10°E and 70°E. Find the distance between them along their parallel of latitude.
    Δλ = 70° − 10° = 60°
    r = 6400 × cos(50°) ≈ 4114 km
    d = (π × 4114 × 60) / 180 ≈ 4 310 km
  8. How many hours correspond to a longitude difference of 60°? Of 22.5°?
    60° ÷ 15 = 4 hours
    22.5° ÷ 15 = 1.5 hours = 1 hour 30 minutes
  9. When it is 7:00 pm Tuesday in Tokyo (UTC+9), what is the time and day in London (UTC+0)?
    Tokyo is 9 hours ahead of London.
    London time = 7:00 pm − 9h = 10:00 am Tuesday
  10. Sydney is UTC+10 and San Francisco is UTC−8. When it is 9:00 am Wednesday in Sydney, what is the time and day in San Francisco?
    Difference: 10 − (−8) = 18 hours (Sydney is 18 hours ahead)
    San Francisco time = 9:00 am Wednesday − 18h = 9:00 am − 18h
    = 9:00 am − 9h = midnight, then − 9 more = 3:00 pm
    = 3:00 pm Tuesday
  11. A flight departs Brisbane (UTC+10) at 6:30 am Monday and arrives in Dubai (UTC+4) after 14 hours. What is the local time and day in Dubai on arrival?
    Departure UTC: 6:30 am − 10h = 8:30 pm Sunday (UTC)
    Arrival UTC: 8:30 pm Sunday + 14h = 10:30 am Monday (UTC)
    Dubai local: 10:30 am + 4h = 2:30 pm Monday
  12. A ship travels along latitude 35°S from 150°E to 70°E (going west). Find the distance travelled.
    Δλ = 150° − 70° = 80°
    r = 6400 × cos(35°) = 6400 × 0.8192 ≈ 5243 km
    d = (π × 5243 × 80) / 180 ≈ 7 321 km
  13. Explain the difference between a great circle route and a parallel route between two cities at the same latitude. Which is shorter and why?
    A great circle route follows the arc of a great circle — the circle whose centre is the centre of Earth. It curves away from the parallel and passes through higher (or lower) latitudes than the two cities.

    A parallel route follows the constant-latitude line (a small circle) directly between the two cities.

    The great circle route is shorter because the great circle is the mathematically shortest path between any two points on a sphere. Small circle routes take a longer curved path around the Earth. This is why airline flights between two cities at the same latitude don’t fly horizontally — they arc toward the poles.
  14. The antipodal point of Sydney (34°S, 151°E) is what coordinate?
    Flip latitude: 34°S → 34°N
    Adjust longitude: 151°E + 180° = 331° → 331 − 360 = −29 → 29°W
    Antipodal point: (34°N, 29°W)
    This is in the Atlantic Ocean, west of Portugal.
  15. A city at 120°E belongs to what UTC time zone (theoretical)? How does the actual time zone of most of Australia differ from this theoretical value?
    Theoretical: 120°E / 15 = UTC+8

    Western Australia does use UTC+8 (AWST). However, eastern Australia (UTC+10, AEST) is theoretically at 150°E, and central Australia (UTC+9:30, ACST) uses a non-standard half-hour offset.

    Time zones don’t follow longitude exactly because they follow political and economic boundaries. Australia chose broader, more convenient zones rather than strictly following 15° divisions.