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.
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 6400 \text{ km}.
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 6400 \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.
Find the distance (to the nearest kilometres) between the following points on the surface of the Earth. Assume the radius of the earth is 6400 \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 6400 \text{ km}:
Honolulu, 21 \degree \text{N}, and Barrow, 71 \degree \text{N}.
Vladivostok, 43 \degree \text{N}, and Darwin, 12 \degree \text{S}.
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 6400 \text{ km}.
Calculate the shortest distance between points A \left( 11 \degree \text{N}, 106 \degree \text{E} \right) andB \left(31 \degree \text{S}, 106 \degree \text{E} \right), given that the radius of the Earth is 6400 \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 6400 \text{ km}.
The Arctic Circle is at a latitude of 66.5 \degree \text{N}. Given that the earth has a radius of approximately 6400 \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}.
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 \text{km}, given that the radius of the Earth is 6400 \text{ km}.
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 6400 \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} |
Quentin wants to know the how long it will take him to travel between Stockholm \left( 59 \degree N, 18 \degree E\right) and Cape Town \left( 34 \degree S, 18 \degree 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.
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 6400 \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.