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Sketching Contour Maps and Determining Radii

The hemisphere is given by f (x,y) = sqrt 64 - x^2 - y^2. Sketch a contour map for this surface using the level curves corresponding to c = 0,1,2,3,4,5,6,7,8

Since this is an example shown in the book, I can see that when c = 8 you draw a circle with a radius of 8 and when c = 0 you have a point at the center of the circle.

I see this but I do not understand how you obtain these radii from the equation.

What is the process used to determine these radii and the the ones between 0 and eight?

Is this process the same for other equations?

Solution Summary

Sketching contour maps and determining radii are investigated. The solution is detailed and well presented.