Answer in Geometry
Let us find the volume of air inside the box. This volume is equal to volume of a parallelepiped. Each box dimension includes relative dimension of this parallelepiped and 2 thicknesses of wood, used to construct the box. (see picture 1 for understanding)
Therefore, this parallelepiped has dimensions (1.5m-2cm)x(0.8m-2cm)x(0.4m-2cm). These are equal to (148cm)x(78cm)x(38cm). The volume of air inside the box is equal to 148cm*78cm*38cm=438672 cm cubed
Volume of the whole box=(volume of air inside the box)+(volume of wood)
(Volume of the whole box)=1.5m*0.8m*0.4m=150cm*80cm*40cm=480000 cm cubed
(Volume of wood, used to construct the box) = (volume of whole box) – (volume of air inside the box)=41328 cm cubed
We assume that mass of air inside the box is negligible in comparison to mass of wood.
mass of box = (volume of wood)*(density of wood)=24796.8 g = 24.8 kg.
Answer: (i) 41328 cm cubed; (ii) 24.8 kg
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