If a cube has surface area SSS and volume VVV, then find the volume of the cube of surface area 3S3S3S.
Answer:
3√3V3√3V3√3V
- Let the edge of the cube be aaa. Then,
Surface area, S=6a2S=6a2S=6a2, and
Volume, V=a3V=a3V=a3. - We can say that a=(S6)12a=(S6)12a=(S6)12. Now let us put this value of aaa in the expression for volume. VVV then becomes:
(S6)32(S6)32(S6)32. - Thus, for another cube with surface area 3S3S3S, the volume will be:
[Math Processing Error] - Hence the volume of the other cube is 3√3V3√3V.