The volume of a cube with side L is given by the equation:
[tex]V=L^3[/tex]
If the side of a cube is dilated by a scale factor k, its new volume V' will be:
[tex]\begin{gathered} V^{\prime}=(kL)^3=k^3L^3=k^3\cdot V \\ \therefore V^{\prime}=k^3V \end{gathered}[/tex]
Then, the volume of the cube scaled up by 12, will be:
[tex]\begin{gathered} V=12^3\times10in^3 \\ =1,728\times10in^3 \\ =17,280in^3 \end{gathered}[/tex]
Therefore, the dilated cube will be able to hold 17,280 cubic inches of water.
