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