The lego has standard brick as shown in the figure.
It comprizes of 8 cylindrical shapes and one rectangular parallelopiped.
The volume of the lego is the volume of 8 cylinders plus the volume of the parallelopiped.
[tex]V_{cyl}=\pi\times r^2\times h=\pi\times(\frac{3}{32})^2\times\frac{1}{16}=\frac{9}{16384}\pi[/tex]So the volume of all cylindrical shapes combined is:
[tex]V_{totcyl}=8V_{cyl}=8\times\frac{9}{16384}\pi=\frac{9}{2048}\pi in^3[/tex]The volume of the paralleopiped is:
[tex]V_p=l\times w\times h=\frac{5}{4}\times\frac{5}{8}\times\frac{3}{8}=\frac{75}{256}in^3[/tex]Hence the total volume is:
[tex]V_{tot}=V_{totcyl}+V_p=\frac{9}{2048}\pi+\frac{75}{256}\approx0.3068in^3[/tex]Hence the volume of water needed to make lego ice cube is 0.3068 cubic inches per brick.
For 10 bricks the water needed will be 3.068 cubic inches.