# A metal cube of edge 12m is melted to form three smaller cubes. If the edge of two smaller cubes are 6m and 8m.Find the surface area of the third smaller cube?

Evaluate: (^{-2}/_{7})^{-4} × (^{-5}/_{7})^{2}

^{ }

^{3}= (12)

^{3 }= 1728m

^{3}

It is melted into three other cubes ,so the volume of the cubes remains same as the volume of bigger cube .

Sides of the smaller cubes are 8m and 6m.

So the volume of the cubes is (8)

^{3}=512m

^{3}

And volume of another cube = 6

^{3}= 216m

^{3}

So total volume = volume of cube of side 8m + volume of side 6m + remaining volume

512 + 216 + remaining volume = 1728

Remaining volume = 1000 m

^{3}

From the remaining volume a cube is formed

So the sides of the third cube is (1000)

^{1/3}= 10m

And the surface area of a cube is given by 6(sides)

^{2}

So the surface area of the third cube = 6(10)

^{2}= 600 m

^{2}

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