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ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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Cubes on a Cube

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

A cube has each of its faces covered by one face of an identical cube, making a solid as shown. The volume of the solid is $875\text{cm}^3$.

What, in $\text{cm}^2$, is the surface area of the solid?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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