Matthew
Smith
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| Posted on Tuesday, 25
May, 2004 - 09:45 pm: |
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There's a formula for the volume of a
rhombic dodecahedron towards the bottom of this page.
The result is that V=(16/9)Ö3a3,
where a is the edge length. If you need to prove this
formula, then you can consider the rhombic
dodecahedron as being made up of a cube of side s, with
a square-based pyramid of height s/2 stuck on each side
(see if you can show that this figure really is a
rhombic dodecahedron), and hence work out a relation
between the volume and side length.
You can work out the volume of gold (because density is
just mass per unit volume, and you know the mass). Hence,
using the formula above, you can find the edge length.
Matthew.
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