Expert: Steve Holleran - 9/19/2007

Question
If I have a sphere of radius r. If I slice the sphere a distance x from the centre of the sphere I am left with a dome. The dome has a circle at it's base with some other radius. I was wondering how do I relate this radius to the original?
Thanks
Chris

Answer
Hi Chris,

Okay, picture a sphere of radius r.  Draw a segment x units long vertically up from the center of the sphere.  Then draw the horizontal radius of the "dome" and call it h.  Then draw a radius of the sphere from the center to where h intersects the sphere.

You basically have a right triangle with legs x and h, and hypotenuse r. So,

                x^2 + h^2 = r^2

                      h^2 = r^2 - x^2

and                     h = sqrt(r^2 - x^2)


Hope this is what you wanted.

Steve