Section of the sphere

Cut the sphere of centre (8, 5, 6) and radius 6 with the horizontal plane z = 6. Find the radius of the section and its area.

Step-by-step solution

Every plane section of a sphere is a circle.
The radius of the section satisfies r² = R² − d², with d the distance from the centre to the plane.
If the plane passes through the centre, the section is a great circle of radius R.
If the plane is tangent (d = R), the section reduces to a point; if d > R, there is no section.

Result: circle of radius 6 u; area 112.52 u².

Do not confuse the radius of the sphere with that of the section: they only coincide in the great circle.