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Question 24
Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.
Solution
Whenever some cubes are melted to form a single larger cube, the total volume always remains constant.
So, Sum of the volumes of three small cubes = Volume of the larger cube.
Let the side of the lager cube so formed be 'a' cm.
Then $$1^3 + 6^3 + 8^3 = a^3$$
$$\Rightarrow a^3 = 729$$
$$\Rightarrow a = 9$$ cm.
Surface area of cube so formed = 6*$$a^2$$ = $$6\times 9^2 = 6\times 81 = 486 cm^2$$
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