Painted Cube

CAT 1996 Slot 1 · QA · Easy · QA

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A cube of side 12 cm12\text{ cm} is painted red on all the faces and then cut into smaller cubes, each of side 3 cm3\text{ cm}. What is the total number of smaller cubes having none of their faces painted?

  1. A.

    16

  2. B.

    8

  3. C.

    12

  4. D.

    24

Answer

B

Explanation

n=12/3=4n = 12 / 3 = 4. Unpainted cubes = (n−2)3=(4−2)3=23=8(n - 2)^3 = (4 - 2)^3 = 2^3 = 8.

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