If a cube has surface area SS and volume VV, then find the volume of the cube of surface area 3S3S.


Answer:

33V33V

Step by Step Explanation:
  1. Let the edge of the cube be aa. Then,
    Surface area, S=6a2S=6a2, and
    Volume, V=a3V=a3.
  2. We can say that a=(S6)12a=(S6)12. Now let us put this value of aa in the expression for volume. VV then becomes:
    (S6)32(S6)32.
  3. Thus, for another cube with surface area 3S3S, the volume will be:
    (3S6)32=(3)32×(S6)32=(3)32V=33V
  4. Hence the volume of the other cube is 33V.

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