Spheres in Cylinder

Geometry Level pending

Imagine a cylinder with a base of radius 1 inscribed in a cone with a base of radius 4 and a height of \( \frac{16}{3}\). Let the space between the cylinder and the cone be filled with spheres of maximum size (all with the same length for their radii), except for the space between the top base of the cylinder and the apex of the cone. Find the total volume of these spheres to one decimal place.

Note: the cross section appears as in the image, which is not to scale

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