Minimization needs imagination

Level pending

Four cubes of volumes 1 c m 3 , 8 c m 3 , 27 c m 3 , 1 cm^3, 8 cm^3, 27 cm^3, and 125 c m 3 125 cm^3 are glued together at their faces. S S in ( c m 2 ) (cm^2) is value of total surface area of the resulting figure. Find minimum possible value of S S .


The answer is 194.

Piyushkumar Palan by Piyushkumar Palan , 31, India

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1 solution

Shaurya Gupta
Jan 3, 2014

Image

The total of surface area of each block = 6 × ( 1 + 4 + 9 + 25 ) = 236 6\times (1 + 4 + 9 + 25) = 236

The surface area eliminated = 2 × ( 3 × ( 1 ) + 2 × ( 4 ) + 1 × ( 9 ) ) = 40 2\times (3\times (1) + 2\times (4) + 1\times (9)) = 40

The minimum surface area, S = 236 − 40 = 194 S = 236 - 40 = \boxed{194}

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