Answer:
The volume of the wood used is ![1,116\ cm^3](https://tex.z-dn.net/?f=1%2C116%5C%20cm%5E3)
Step-by-step explanation:
<u>The Volume of a Rectangular Cuboid</u>
In a rectangular cuboid, all angles are right, and the opposite faces are equal.
The volume of a cuboid of dimensions a,b,c is:
V=a.b.c
The rectangular box is made of wood with externals dimensions of 25 cm by 20 cm by 15 cm.
The external volume of the box is:
![V_e=(25)*(20)*(15)=7,500\ cm^3](https://tex.z-dn.net/?f=V_e%3D%2825%29%2A%2820%29%2A%2815%29%3D7%2C500%5C%20cm%5E3)
The walls of the box are 0.5 thick each, this means that the internal dimensions are 1 cm less than the external dimensions, including the lid.
Thus the internal volume is:
![V_i=(24)*(19)*(14)=6,384\ cm^3](https://tex.z-dn.net/?f=V_i%3D%2824%29%2A%2819%29%2A%2814%29%3D6%2C384%5C%20cm%5E3)
The volume of the wood used is the difference between the external and the internal volumes:
![V_w=7,500\ cm^3-6,384\ cm^3=1,116\ cm^3](https://tex.z-dn.net/?f=V_w%3D7%2C500%5C%20cm%5E3-6%2C384%5C%20cm%5E3%3D1%2C116%5C%20cm%5E3)
The volume of the wood used is ![\mathbf{1,116\ cm^3}](https://tex.z-dn.net/?f=%5Cmathbf%7B1%2C116%5C%20cm%5E3%7D)