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Cubes required to cover a large cube

CMAT 2018 · Logical Reasoning · Medium · Cubes and Dice

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125 small but identical cubes have been put together to form a large cube. How many such small cubes will be required to cover this large cube completely?

  1. A.

    208

  2. B.

    212

  3. C.

    254

  4. D.

    218

Answer

D

Explanation

The large cube consists of 5×5×5=1255 \times 5 \times 5 = 125 cubes. To cover it completely with 1 layer of small cubes, the new outer dimension becomes (5+2)×(5+2)×(5+2)=7×7×7=343(5+2) \times (5+2) \times (5+2) = 7 \times 7 \times 7 = 343 cubes. Number of new small cubes required = 343−125=218343 - 125 = 218.

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