# A (somewhat) generalisation

Geometry Level pending

Imagine a 3-D polyhedron. This polyhedron has to be a convex polyhedron and a sphere can be inscribed in this polyhedron with all of the polyhedron's faces tangent to the sphere. This sphere has radius $$r$$.

By a method, let's say displacement, we get that the volume of this polyhedron is $$v$$.

Therefore, what is the surface area of this shape? (Also, the material to make up this shape is not soluble in water)

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