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How do I find the circumference of the circle of latitude 40 degress North?

Hi, I'm doing a maths assignment and have no clue how to answer this question.Please Help!!!! The question is: Find the circumference of the circle of latitude 40 degress North. Take the radius of the earth as 6350 km.

Public Comments

1. that's cheating
2. If the radius of the earth at the equator is r, then the radius at 40° N latitude is r*cos(40°). I trust you can take it from there.
3. Use interpolation. If the radius is 6350km at 0 degrees, and the radius is 0 at 90 degrees, and the degrees are at equal intervals, then you know that at 40 degrees North the radius will be 6350km-4/9(6350km), or 5/9*6350km. Now just plug the new found radius into the circumference equation.
4. Draw a circle representing the earth, with a horizontal line through the equator. Draw a second line from the centre at an angle of 40 degrees. Draw a vertical line from where the 40 degree line cuts the circle, down to the equator This is to see what goes on. You can see that the radius at angle 40 degrees is the hypotenuse We need the length of the line from the centre of the equator to where the vertical line intersects it to form a right angled triangle. This will be radius times cos 40 Cos is adjacent over hypotenuse and the hypotenuse is 6350 6350 cos 40 = 6350 * 0.7660 = 4864.382 km Diameter = 2pi * 4864.382 = 30,576..12 using 22/7 for PI