Expert: Steve Holleran - 7/7/2007

Question
what is the radius of the circle formed when a plane cuts a sphere of radius 23 and distance 10 from it's center? what would be the approximate volume of a slice of thickness .345 which is cut at this distance from the center?

Answer
Hi Jessica,

Okay, I'm assuming that we are slicing with a plane that is perpendicular to a radius.

If so,  then let's draw the sphere, and a horizontal radius from the center to the "right-hand" edge.  If we go out 10 from the center and then a vertical segment, then go back to the center from there, we should have a right triangle.

The hypotenuse is 23, the radius of the sphere, and the base is 10.  Call the vertical side x.  So we have:

                10^2 + x^2 = 23^2

                 100 + x^2 = 529

                so      x^2 = 429.

Taking the square root, the radius of the circle would be 20.7.  

For the other question, the volume would be the cross-section area of the circle times the thickness of 0.345.

The calculation is :     V = pi * 20.7^2 * 0.345

and I got                V = 464.97

I hope this is what you needed.

Steve Holleran