Question 43

Three cubes of volume $$1cm^{3}$$ , $$216cm^{3}$$ and $$512cm^{3}$$ are melted to form a new cube. What is the diagonal of the new cube?

Solution

The volume of the new cube is equal to the sum of volumes of the three cubes i.e., volume of the new cube = 1+216+512 = 729 $$cm^3$$

The volume of cube of side a is given by $$a^3$$

=> $$a^3$$ = 729

=> a = 9

Therefore, the side of new cube is 9 cm.

Length of diagonal of cube = $$\sqrt{3}a$$

Length of diagonal of new cube = $$9\sqrt{3}$$ cm

The answer is option A.

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