Problem 58409. Calculate the volume of the intersection of two balls

Consider two balls (solid spheres) in , with radius and respectively. Suppose that the distance between the centers of the two balls is . Please find the volume of the intersection of the two balls.
Illustration:
[X, Y, Z] = sphere(36);
r1 = 1;
r2 = 0.8;
c2 = [0.6 -0.8 0];
surf(X * r1, Y * r1, Z * r1)
hold on
surf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))
hold off
axis equal
Solve

Solution Stats

40.0% Correct | 60.0% Incorrect
Last Solution submitted on Sep 01, 2025

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geometry

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