The weight of a piece of crystal in the form of a regular dodecahedron is 360 lbs., and each of its edges is 10 inches long. What is the weight of a similar piece of crystal whose edge edge measures 16 in.?

Question

directrix · Answer

The two regular polyhedra of this problem are similar dodecahedrons. 

Theorem: The cube of the scale factor of two similar solids is equal to the ratio of the volumes of the two solids.

directrix · Answer

Therefore,

(10/16) ^3 = 360/w where w is the weight of the dodecahedron with edge 16.

directrix · Answer

(10/16) ^3 = 360/w

(5/8) ^ 3  = 360 / w

125/512 = 360/w

Your task: solve for w

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