Question

Three cubes of volume 1, 8 and 27 are glued together at their faces. The smallest possible surface area of the resulting configuration is
A) 36
B)56
C)70
D)72​

Answer 1

Answer:

The smallest possible surface area of the resulting configuration is 70.

Step-by-step explanation:

Step 1: Consider just one face of the cubes, they have to be glued. If the smaller is put smack dab, consider that the standard surface area. The exposed surface area on that glued face only is

exposed=9-4=5

Step 2: But what if the don't overlap exactly, one hangs over the side of the other.

let x be the overhang.

surface area on the joined surface of the smaller cube is 2x

and the surface area on the joined surface of the larger cube is 9-(2-x)2

Step 3: Total= 2x+9-4+2x=5+4x so the minumum surface area on that surface will be 5

total surface of this configuration:

5+5*9+5*4=70sqr units

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