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 r .

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

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

v 3 r \frac {v}{3r} 3 v r \frac {3v}{r} 3 r v \frac {3r}{v} r 3 v \frac {r}{3v}

Aloysius Ng by Aloysius Ng , 20, Singapore

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