Let the inner dimensions of the box be L, W, H standing for length, and height. The thickness of the wood is T. We can put figures in later. The inner volume is LWH. This is all empty space. The question doesn't state whether the box is completely closed or open, so we'll go for each in turn.
Box (with lid): the outer dimensions are L+2T, W+2T, H+2T so the outer volume is (L+2T)(W+2T)(H+2T), and the volume of wood is outer volume minus inner volume=(L+2T)(W+2T)(H+2T)-LWH=
2T(LH+WH+LW+2T(L+W+H)+4T^2) m^3.
Open box (no lid): outer dimensions are L+2T, W+2T, H+T and outer volume is (L+2T)(W+2T)(H+T)
Outer-inner: T(2LH+2WH+LW+2T(L+W+2H)+4T^2) m^3.
Cost is Rs 5400 times the volume.
Now we need to replace L, W and H. But here's the problem: the thickness of the wood is given as 2.5m, which seems excessive, so let's replace it with 2.5cm. The dimension 2.4cm of length width or height seems very small compared to the other dimensions, so let's replace it with 2.4m. This is a more realistic set of dimensions. If the box is closed, the volume is 0.979875 m^3 so the cost of the wood is Rs5291.33.
Let's assume that the smallest measurement is the height of the box, H.
The open box has a volume of 0.7318125 m^3 and the cost is Rs3951.79.
CHECK: Using the assumptions about the dimensions, the inner volume is 14.4 m^3. The outer volume of the closed box is 4.05*2.45*1.55=15.379875 m^3 and the open box is 4.05*2.45*1.525=15.1318125 m^3. Take away the inner volume: 0.979875 (closed), 0.7318125 (open) cubic metres. And the cost is Rs5291.325 (closed), Rs3951.7875 (open).
