A co-worker posed this problem to me, and I gave him the following answer, mostly pulled from my ass. Is it the right answer? If not, what is? OK....you've got a sphere. You want to cut off a portion of the sphere at Line L (I guess it's a plane, reall). How do you figure out the surface area of that sphere? My answer: The formula for surface area of a sphere is 4 x pi x radius squared. For the top half of the sphere, the formula is 2 x pi x radius squared. You need a Multiplier for that half of the sphere to find the area of the cut-off portion. Now, in order to find the Multiplier, you draw a line out from the center of the sphere along the "x-axis", and then draw another line from the center of the sphere to the intersection of the plane and the sphere: Chord C. Now, you figure the cosine of Angle A, and multiply it by half of the area of the sphere. There's your answer. Correct? My reasoning is, if the "cut-off plane" is right at the center of the circle, your multiplier is 1 (or the cosine of 0). If the plane is tangent to the sphere, right at the top of the sphere, your multiplier is 0 (or the cosine of 90). It's tough to explain my thought process on the intraweb. But can anyone prove or disprove my theorem?