Question 31

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?

Solution

125 small cubes have been together, so we have a 5x5x5 cube.

So,if we want to cover it completely we've need to cover all the sides of it completely, we will just put same cubes over the one of the sides of it and then from both the sides we've to spread it just by one row and so it will cover it properly, and do it for all the other sides.

So, now we will have a 7x7x7 cube.

Thus, number of cubes required to cover it = $$(7\times7\times7)-(5\times5\times5)=218$$

=> Ans - (D)

In short, to cover it completely, cubes required = $$(n+2)^3-(n)^3$$

and to make it hollow, cubes removed = $$(n)^3-(n-2)^3$$

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