A cube of side $12$ $c m$ , is painted red on all the faces and then cut into smaller cubes, each of side $3 c m$ . What is the total number of smaller cubes having none of their faces painted?

16

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8

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12

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24

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Solution

The correct option is D $8$
Volume of Cube $= n \times$ (Volume of small cubes)
So $(12)^{3} = n \times 3^{3}$
$n = 64$
One edge is divided into $\frac{12}{3} = 4$ parts, hence each face will have $4 \times 4 = 16$ small cubes.
Now the number of cubes exposed on the faces will be painted. So $16$ at front, $16$ at back and $6$ in each of the remaining $4$ layers .
So the rest cubes left without getting painted is $64 - 16 - 16 - 24 = 8$

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

A cube of side $12$ $c m$ , is painted red on all the faces and then cut into smaller cubes, each of side $3 c m$ . What is the total number of smaller cubes having none of their faces painted?