How can contour map data be used to determine volume?

[brandy]

if you are given a contour map how could you calculate the volume of the hill.

 

[mgb_phys]

Roughly you would work out the area of each contour line and multiply by the distance between lines.
There is an interesting law for the area of any polygon if you are given the contours as line segments.

 

[brandy]

they'r ellipses but id still like to hear it

 

[mgb_phys]

If you have the x,y coordinates of each vertex of a polygon then
Area = (x0y1 + x1y2 + ... + xn-1y0 - y0x1 - y1x2 - ... - yn-1x0) / 2

It doesn't matter what shape it is (doesn't have to be convex) as long as the sides don't
cross each other.

 

[brandy]

what exactly do u mean by x0 and x1 and y0 and etc

 

[mgb_phys]

The coordinates of each vertex of the polygon, ie x0,y0 is the first corner, x1,y1 is the second etc..
The nice thing is that you don't have to calculate any lengths or angles.