Question

how many small cubes each of 96 sq. cm surface area can be made from the material obtained by melting a larger cube of 384 cmsq surface area

Answer 1

hope it's correct........

Answer 2

The number of cubes each of 96 sq. cm surface area can be made from the material obtained by melting a larger cube of 384 cmsq surface area is 8

Step-by-step explanation:

Let the side of the larger cube be A cm

Then the surface area of the cube $=6A^2$

According to the question

$6A^2=384$

$\implies A^2=64$

$\implies A=\sqrt{64}=8$ cm

Volume of the larger cube

$V=A^3$

$\implies V=8^3$

$\implies V=512$ cubic cm

Similarly if the side of the smaller cube is a cm

Then

Surface area = 96 sq cm

or, $6a^2=96$

or, $a^2=16$

or, $a=4$

Threfore, volume of the smaller cube

$V'=a^3$

$\implies V'=4^3=64$ cubic cm

The number of smaller cubes that can be made by melting the larger cube

$=\frac{V}{V'}$

$=\frac{512}{64}$

$=8$

Hope this answer is helpful.

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