Find the circumference of a great circle around a sphere with radius r = 4 \text{ cm}. Round your answer to two decimal places.
Find the circumference of a great circle around a sphere with a diameter of 4 \text{ km}. Round your answer to two decimal places.
Find the circumference of a small circle with a radius of 2 \text{ m} that lies on a sphere with a radius of 3 \text{ m}. Round your answer to two decimal places.
If Mercury has a radius of 2878 \text{ km}, find the circumference of a great circle that lies on its surface. Round your answer to one decimal place.
State whether each of the following is a small or great circle:
The 40 \degree \text{S} parallel
The 20 \degree \text{W} meridian
Find the circumference of the small circle in the image.
Round your answer to two decimal places.
In the following diagram, an arc of a small circle has been drawn in red:
Find the length of the arc correct to two decimal places.
Great circles contain the diameter of the sphere they're drawn onto, small circles do not. Determine whether each of the following is a great circle or a small circle:
The 10 \degree \text{W }meridian.
The 50 \degree \text{N }parallel.
The 70 \degree \text{E } meridian.
The 80 \degree \text{S } parallel.
Consider the following figure:
Consider the following two locations on Earth, \left( 30 \degree \text{S}, 70 \degree \text{E} \right)and \left( 70 \degree \text{S}, 70 \degree \text{E} \right). Do they lie along the same meridian or the same parallel?
Do \left( 10 \degree \text{S}, 70 \degree \text{E}\right)and \left( 10 \degree \text{S}, 30 \degree \text{E}\right) lie along the same meridian or the same parallel?
Does a parallel form a great circle or small circle?
Does a meridian form half of a small circle or half of a great circle?
Find the angular distance between the following:
A hiker is orienteering and travels due south for 277.5 \text{ km}, how many degrees south has their coordinate position changed to one decimal place?
The coordinates of two cities A and B are (32 \degree \text{S}, 84 \degree \text{E}) and (22 \degree \text{S}, 84 \degree \text{E}).
State whether the following is a great circle that passes through cities A and B:
10 \degree \text{S}
84 \degree \text{E}
32 \degree \text{S}
54 \degree \text{S}
Find the angular distance between the two cities.
Find the shortest distance between the two cities to the nearest kilometre, given that the radius of the Earth is 6371 \text{ km}.
The angular distance between points A and B on the Earth’s surface is 148 \degree.
The radius of the Earth is 6371 \text{ km} to the nearest kilometre. Find the radius of the Earth to the nearest hundred kilometres.
Hence, calculate the arc length AB to the nearest kilometre.
Consider the two points with coordinates of \left(39\degree \text{N}, 121 \degree \text{E} \right) and \left(24\degree \text{S}, 121 \degree \text{E} \right).
Using the approximation that the radius of the earth is 6371 \text{ km}, find the distance between them to the nearest kilometre.
The coordinates of two cities A and B are (43 \degree \text{N}, 30 \degree \text{W}) and (37 \degree \text{S}, 30 \degree \text{W}) respectively.
State the city that is closest to the prime meridian.
Find the shortest distance between the two cities to the nearest kilometre, using 6400 \text{ km} as the radius of the Earth.
A more accurate radius of the Earth is 6371 \text{ km}. Find the shortest distance between the two cities using this radius to the nearest kilometre.
Calculate the difference between these two measurements of the shortest distance between the cities.
The coordinates of the Devil's Sea are (58 \degree \text{N}, 170 \degree \text{E}). If you drew a line from this position through the centre of the Earth and out the other side of the Earth, you’d end up at point B.
Find the shortest distance along the earth's surface between the Devil's Sea and point B, given that the radius of the Earth is 6371 \text{ km}.
A sailor started his journey from position \left(27 \degree \text{N},146 \degree \text{E} \right) and continued along the same line of longitude until he arrived on an island with a latitude of 18 \degree \text{N}.
Find the angular distance he covered.
Find the distance he covered to the nearest kilometre, given that the radius of the Earth is 6371 \text{ km}.
Find the distance (to the nearest kilometres) between the following points on the surface of the Earth. Assume the radius of the earth is 6371 \text{ km}.
Find the distance, to the nearest kilometre, between the following cities, given that the cities lie on the same north-south line and the radius of Earth is 6371 \text{ km}:
Honolulu, 21 \degree \text{N}, and Barrow, 71 \degree \text{N}.
Vladivostok, 43 \degree \text{N}, and Darwin, 12 \degree \text{S}.
A plane flies due South, from Cairns to Townsville. The table attached displays the coordinates of each city:
What is the distance the plane has travelled to the nearest kilometre?
Assume the radius of the Earth is 6371 \text{ km}.
| \text{Cairns} | 16 \degree \text{S} | 145 \degree \text{E} |
| \text{Canberra} | 35 \degree \text{S} | 148 \degree \text{E} |
| \text{Geelong} | 43 \degree \text{S} | 144 \degree \text{E} |
| \text{Hobart} | 42 \degree \text{S} | 148 \degree \text{E} |
| \text{Melbourne} | 37\degree \text{S} | 144 \degree \text{E} |
| \text{Portland} | 45 \degree \text{N} | 122 \degree \text{W} |
| \text{San Francisco} | 37 \degree \text{N} | 122 \degree \text{W} |
| \text{Seattle} | 47 \degree \text{N} | 122 \degree \text{W} |
| \text{Townsville} | 19 \degree \text{S} | 145 \degree \text{E} |
| \text{Vancouver} | 49 \degree \text{N} | 122 \degree \text{W} |
Find the distance between Ho Chi Minh City \left( 10 \degree \text{N}, 106 \degree \text{E} \right) and Jakarta \left( 6 \degree \text{S}, 106 \degree \text{E} \right) correct to the nearest kilometre. Approximate the radius of the Earth as 6371 \text{ km}.
Calculate the shortest distance between A \left( 11 \degree \text{N}, 106 \degree \text{E} \right) and B\left(31 \degree \text{S}, 106 \degree \text{E} \right), l, given that the radius of the Earth is 6371 \text{ km}.
A location has coordinates \left(41 \degree \text{S}, 85 \degree \text{W} \right). If l is its distance from the equator, find l correct to the nearest kilometre, given that the radius of the Earth is 6371 \text{ km}.
The Arctic Circle is at a latitude of 66.5 \degree \text{N}. Given that the earth has a radius of approximately 6371 \text{ km}, what is the shortest distance, to the nearest kilometre, from any point on the Arctic Circle to:
The Equator.
The Antarctic Circle, which is at a latitude of 66.5 \degree \text{S}.
Consider the two locations A\left( 25 \degree \text{N}, 70 \degree \text{E}\right) and B\left( 25 \degree \text{N}, 150 \degree \text{E}\right).
Do the two locations A and B lie on the same meridian or parallel?
Does a parallel form a great circle or small circle?
How far east of point A is point B? Give your answer in degrees.
Find the distance between the two locations along the parallel, correct to the nearest kilometre. Use D = 111.2 A \cos B, where B is the latitude and A is the angular distance.
A sailor started their journey from position \left( 40 \degree \text{S}, 168 \degree \text{E}\right) and continued along the same line of longitude until they arrived on Norfolk Island with a latitude of 29 \degree \text{S}.
How many kilometres will they cover for each degree change in longitude? Give your answer to one decimal place. Consider the radius of the Earth to be 6371 \text{ km}.
If he covered D \text{ km}, find D to the nearest kilometre. Use the formula D = 111.2 \times \theta.
Calculate the shortest distance, D, for each of the Following pairs of points. Round your answers to the nearest kilometre. Use the formula D = 111.2 \times \theta.
A\left( 20 \degree \text{N}, 60 \degree \text{E} \right) and B\left( 20 \degree \text{S}, 60 \degree \text{E} \right)
A\left( 66 \degree 35 ' \text{ S}, 42 \degree 40 ' \text{ W} \right) and B\left( 12 \degree 5 ' \text{ S}, 42 \degree 40 ' \text{ W} \right)
A\left( 42 \degree 15 ' \text{ N}, 36 \degree 55 ' \text{ W} \right) and B\left( 30 \degree 5 ' \text{ S}, 36 \degree 55 ' \text{ W} \right)
Consider the points A\left( 20 \degree \text{S}, 40 \degree \text{W}\right) and B\left( 20 \degree \text{S}, 85 \degree \text{W}\right).
Calculate the radius, correct to two decimal places, of the circle which forms the \left( 20 \degree \text{S}\right)parallel. Consider Earth’s radius to be 6371 \text{ km}.
Hence, find the distance between the two positions along their common parallel, correct to the nearest kilometre.
Consider the points A\left( 40 \degree \text{S}, 40 \degree \text{E} \right) and B\left( 40 \degree \text{S}, 75 \degree \text{E}\right).
Calculate the radius of the circle which forms the \left( 40 \degree \text{S}\right) parallel. Assume the Earth's radius equals 6371 \text{ km}. Round your answer to two decimal places.
Hence, find the distance between the two positions along their common parallel, correct to the nearest kilometre.
Consider the point A\left( 40 \degree \text{N}, 10 \degree \text{W} \right).
Calculate the radius of the circle which forms the \left( 40 \degree \text{N}\right) parallel. Assume the Earth's radius equals 6371 \text{ km}. Round your answer to two decimal places.
Hence, find the distance that point A is from the Prime Meridian along the parallel, correct to the nearest kilometre.
Calculate the distance between the following points along their common parallel, using D = 111.2 \cos \theta \times \omega where \omega is the angular distance and \theta is the angle of latitude. Round your answers to the nearest kilometre.
A\left( 85 \degree \text{S}, 25 \degree \text{W}\right) and B\left( 85 \degree \text{S}, 60 \degree \text{W}\right)
A\left( 15 \degree \text{N}, 35 \degree \text{W}\right) and B\left( 15 \degree \text{N}, 70 \degree \text{W}\right)
A \left( 55 \degree \text{S}, 45 \degree \text{E}\right)and B\left( 55 \degree \text{S}, 165 \degree \text{W}\right)
A\left( 65 \degree \text{N}, 55 \degree \text{E}\right)and B\left( 65 \degree \text{N}, 150 \degree \text{W}\right)
A\left( 66 \degree 15 ' \text{ S}, 78 \degree 36 ' \text{ E}\right) and B\left( 66 \degree 15 ' \text{ S}, 32 \degree 12 ' \text{ E}\right)
A\left( 54 \degree 39 ' \text{ N}, 25 \degree 42 ' \text{ W}\right) and B\left( 54 \degree 39 ' \text{ N}, 34 \degree 6 ' \text{ E}\right)
Consider the two points with coordinates of \left(9 \degree \text{S}, 58 \degree \text{W} \right) and \left( 8 \degree \text{N}, 58 \degree \text{W} \right). Assume the radius of the Earth is 6371 \text{ km}.
Find the time it will take to fly between the two points if the plane travels at a speed of 640\text{ km/h}. Give your answer in hours correct to two decimal places.
Luke wants to know the how long it will take him to travel between Nanjing\left( 32 \degree \text{N}, 118 \degree \text{E}\right)and Port Hedland \left( 20 \degree \text{S}, 118 \degree \text{E} \right).
Find the distance between the two cities using the formula D = 111.2 \times A where D is the total distance in kilometers, and A is the angular distance.
Hence, find the time it will take to fly between the two cities if the plane travels at a speed of 610 \text{ km/h}. Give your answer in hours correct to two decimal places.
Quentin wants to know the how long it will take him to travel between Stockholm \left( 59 \degree \text{N}, 18 \degree \text{E}\right) and Cape Town \left( 34 \degree \text{S}, 18 \degree \text{E}\right).
Find the time it will take to fly between the two cities if the plane travels at a speed of 720 \text{ km/h}. Give your answer in hours correct to two decimal places.
Skye wants to know the how long it will take her to travel between Nanjing \left( 32 \degree \text{N}, 118 \degree \text{E}\right) and Port Hedland \left( 20 \degree \text{S}, 118 \degree \text{E}\right).
Find the time it will take to fly between the two cities if the helicopter travels at a speed of 300 \text{ km/h}. Give your answer in hours correct to two decimal places.
Kenneth wants to know the how long it will take him to travel between Helsinki \left( 60 \degree \text{N}, 25 \degree \text{E} \right) and Port Elizabeth \left( 34 \degree \text{S}, 25 \degree \text{E}\right).
Find the time it will take to fly between the two cities if the plane travels at a speed of 620 \text{ km/h}. Give your answer in hours correct to two decimal places.
Two cities located almost directly on the equator are Libreville, Gabon at 10 \degree \text{E}and Kismayo, Somalia at 45 \degree \text{E}.
Find the distance between the two cities, correct to the nearest kilometre. Use the formula D = 111.2 \times A where A is the angular distance.
Ben wants to know the how long it will take him to travel between Sydney, Australia \left( 34 \degree \text{S}, 151 \degree \text{E} \right) and Cape Town, South Africa \left( 34 \degree \text{S}, 18 \degree \text{E} \right).
Find the time it will take to fly between the two cities if the plane travels at a speed of670 \text{ km/h} keeping the same latitude. Round your answer to two decimal places.
The Antarctic circle is located at 66.5 \degree \text{S} and the Arctic circle is located at 66.5 \degree \text{N}.
Calculate the radius, to two decimal places, of the circles. Assume Earth’s radius to be 6371 \text{ km}.
If you were to take a flight following the boundary of either circle, what distance would this flight cover to the nearest kilometre?
If a small plane travels at a speed of 260 \text{ km/h}, how long would a flight around either circle take? Give your answer to one decimal place.
Brisbane is located on the 27.5 \degree \text{S} parallel and Melbourne is located on the 37.8 \degree \text{S} parallel. Assume 6371 \text{ km} is the Earth's radius.
Find the distance a flight from Melbourne would travel non-stop around the globe on the 37.8 \degree \text{S} parallel before landing back in Melbourne, to the nearest kilometre.
If a plane travels at 390 \text{ km/h}, how long will a similar trip departing from Brisbane take? Give your answer to two decimal places.
Ned wants to fly from Newcastle \left( 32.4 \degree \text{S}, 151.8 \degree \text{E}\right) to Perth \left( 32.4 \degree \text{S}, 115.5 \degree \text{E}\right) and then on to Denpasar \left( 8.6 \degree \text{S}, 115.5 \degree \text{E}\right).
Estimate the total flight time to for the journey if the plane flies at an average speed of 790 \text{ km/h}. Give your answer in hours correct to two decimal places.