Block Builder

Geometry Level 2

You make a 3D figure by first putting down a 3x3 layer of unit blocks.

On top of this layer, you place three more unit blocks such that they can only go directly on already existing blocks, with no overlapping; they cannot stack on top of each other, so there will be 2 layers only at the end.

How many different possible surface areas are there for the final 3D figure?

3 2 5 4

Jason Dyer by Jason Dyer

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2 solutions

Amer Ahmed
Nov 1, 2016

We can add three unit cubes in three different ways to make a distinct surface area : 1- no two cubes share a common surface. 2- only two cubes share a common surface. 3- one cube shares a common surface with both of the rest two cubes. So we have three different configurations for the last 3D surface area.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Geoff Pilling
Nov 1, 2016

The area will be the same except for the extent to which the placed blocks overlap each other. There are separate ways that the three blocks on top can overlap. (1) No overlap. (2) Two blocks overlap by one square and one doesn't. And, (3) Two both overlap with a common block. Therefore there are 3 \boxed3 different final surface areas.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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