If a cube has surface area ^@S^@ and volume ^@V^@, then find the volume of the cube of surface area ^@3S^@.


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Answer:

^@3 \sqrt{ 3 }V^@

Step by Step Explanation:
  1. Let the edge of the cube be ^@a^@. Then,
    Surface area, ^@S = 6a^2^@, and
    Volume, ^@V = a^3^@.
  2. We can say that ^@a = \left(\dfrac{ S } {6} \right)^{ 1 \over 2 }^@. Now let us put this value of ^@a^@ in the expression for volume. ^@V^@ then becomes:
    ^@\left(\dfrac{ S } {6}\right)^{ 3\over 2 }^@.
  3. Thus, for another cube with surface area ^@3S^@, the volume will be:
    ^@\begin{align} &\left(\dfrac{ 3S } {6}\right)^{ 3 \over 2 } \\ = & ( 3 )^{ 3 \over 2 } \times \left(\dfrac{ S } {6}\right)^{ 3\over 2 } \\ = & ( 3 )^{ 3 \over 2 }V \\ = & 3 \sqrt{ 3 }V \end{align}^@
  4. Hence the volume of the other cube is ^@3 \sqrt{ 3 }V^@.

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