There are 2 spheres one with a radious "r1" and an other with the radious "r2". These spheres overlap to create a shape with 2 faces and 1 edge called a disk. The distance between the center of each face on a disk is "d". One can calculate the volume of a disk using "r1", "r2", and "d". What is the formula to calculate the disk's volume with the values of "r1", "r2", and "d"?This image is a model of the problem
2026-04-20 10:01:22.1776679282
Volume of the overlap between 2 spheres
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According to Wolfram mathworld of which the derivation can be found on that page, the volume is
$$V=\frac{\pi(r_1+r_2-D)^2(D^2+2D(r_1+r_2)-3(r_1^2+r_2^2)+6r_1r_2)}{12D}$$
where $D$ is the distance between two centers.
The volume is obtained by adding the volumes of two spherical caps.
If they intersect, then
$$D= (r_1-d)+d+(r_2-d)=r_1+r_2-d$$