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Volume of a cuboid

Q. A large cu...

Question

Q. A large cube with side 9 cm is colored red on all faces, and then is cut into small identical cubes of 1.5 cm side each. Now, how many small cubes will not have any face colored?

A

343

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B

729

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C

125

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D

64

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Solution

The correct option is D 64
$n = \frac{9}{1.5} = 6$

small cubes with no face coloured $= (n - 2)^{3}$

$= (6 - 2)^{3}$

$= 4^{3} = 64$

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