How many small cubes,each of 96,cm^{2} surfac | vedclass

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(A) The surface area of a cube is given by $6a^{2}$,where $a$ is the edge length.For the small cube: $6a_{s}^{2} = 96 \implies a_{s}^{2} = 16 \implies

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$8$

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(A) The surface area of a cube is given by $6a^{2}$,where $a$ is the edge length.For the small cube: $6a_{s}^{2} = 96 \implies a_{s}^{2} = 16 \implies a_{s} = 4\,cm$.The volume of the small cube is $V_{s} = a_{s}^{3} = 4^{3} = 64\,cm^{3}$.For the large cube: $6a_{L}^{2} = 384 \implies a_{L}^{2} = 64 \implies a_{L} = 8\,cm$.The volume of the large cube is $V_{L} = a_{L}^{3} = 8^{3} = 512\,cm^{3}$.The number of small cubes that can be formed is $\frac{V_{L}}{V_{s}} = \frac{512}{64} = 8$.

How many small cubes,each of $96\,cm^{2}$ surface area,can be formed from the material obtained by melting a larger cube with $384\,cm^{2}$ surface area?

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