Shyam wants to make a sold brick shape structure from $400$ wooden cubes of unit volume each. If the sides of the solid brick have the ratio $1:2:3$, then the maximum number of cubes, which can be used will be

Let the dimensions of the brick be x, 2x and 3x, so its total volume is 6 times x cubed. Since each wooden cube has a unit volume, the maximum number of cubes that can form this specific solid structure is 6 times x cubed. Testing integer values shows that when x is 4, the solid uses 384 cubes, which is the maximum possible without exceeding the available 400 cubes.

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