A geographical globe has a radius of 18cm.find the radius of the circleformed by the parallel of latitude 56 degrees south.
2pi*18*cos56
i dont now
To find the radius of the circle formed by the parallel of latitude 56 degrees south, we need to consider the geometry of a sphere.
1. Start by visualizing a geographical globe with a radius of 18 cm.
2. Recall that lines of latitude are parallel circles that run horizontally around the globe.
3. The equator is considered 0 degrees latitude, and the North Pole is 90 degrees latitude. Since we're looking for the radius of a parallel of latitude 56 degrees south, we need to find the radius of the circle that lies 56 degrees south of the equator.
4. Notice that the distance from the equator to the 56th parallel of latitude will be the same as the distance from the 56th parallel to the South Pole. This is because latitude lines are evenly spaced.
5. Calculate the angle between the equator (0 degrees latitude) and the 56th parallel (56 degrees latitude) using subtraction: 56 - 0 = 56 degrees.
6. To find the radius of the circle formed by the 56th parallel of latitude, use the formula:
r = (latitude in degrees / 360 degrees) * (circumference of the globe)
In our case:
r = (56 degrees / 360 degrees) * (2 * π * 18 cm)
r = (56/360) * (2 * 3.14 * 18 cm)
7. Calculate the result:
r = (0.1556) * (113.04 cm)
r ≈ 17.58 cm
Therefore, the radius of the circle formed by the parallel of latitude 56 degrees south is approximately 17.58 cm.