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Calculate volume of spherical cap (membrane under pressure)

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A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between the end of the glass pipe and piece of membrane. Need a solution in matlab.

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Solution:

Note that the volume in question is the difference between a circular sector of a sphere and a cone, both having their tips at the center of the sphere.

Let us look at an axial section of the body by a plain as in the figure:

Let "r" be the radius of the sphere and let "a" be the central angle based on half the arc.
Then the diameter of the tube, D = 3 mm, and ...

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