Explanation:

The largest rectangular solid that could be placed inside the tank is one with all the vertices on the curved surface of the tank
i.e. Diameter of the circular base = Diagonal of the rectangular face
\(12 = \sqrt{l^2 + b^2}\)

Also, the volume would be maximum when the solid is square faced with height equal to that of cylindrical tank.
Therefore, \(l = b = a\)
i.e. \(12 = \sqrt{a^2 + a^2}\)
\(a = \frac{12}{\sqrt{2}}\)

Now, the volume = \(a^2H = (\frac{12}{\sqrt{2}})^2(10) = 720\)

Hence, option E