Two cubes of volumes 8cm3 and 27cm3 are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid

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Mathematics

Jakob Dillon

Yesterday, 06:57

Two cubes of volumes 8cm3 and 27cm3 are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid

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Rene Houston · Answer 1

70

Step-by-step explanation:

First, we note that the cubes of volume 8 and 27 must have edges of length 2 and 3, respectively.

the surface area of 3x3x3 cube is 6*9=54 the surface area of 2x2x2 cube is 6*4=24

If not joined, total area is 78

The maximum concealed surface area is an entire face of the 2-cube, on both solids: 2*4 = 8

So, the minimum exposed area would be 78-8 = 70