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From a $10 × 10 × 10$ cube which is formed by combinations of $1 × 1 × 1$ cubes a layer of the smaller cubes is removed. What will be the number of $1 × 1 × 1$ cubes present in this new cube?

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900

488

512

729

answer is C.

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Detailed Solution

10 × 10 × 10

cube has 10 cubes of

1 × 1 × 1

cubes each along its length, breadth, and width.
If we take away a layer of

1 × 1 × 1

cubes (the smaller cubes), the new cube will have the following dimensions:
Length,

10 − 1 − 1 = 8

.
Breadth,

10 − 1 − 1 = 8

.
Width,

10 − 1 − 1 = 8

.
So, the number of

1 × 1 × 1

cubes in this

8 × 8 × 8

cube equals,

= 8 × 8 × 8 = 512

Hence, the correct option is 3.

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