A closed wooden box measures externally 10 cm long, 8 cm broad and 6 cm high. If the thickness of the wood is 0.5 cm, then the volume of wood required is:

Length (L) = 10 cm
Breadth (B) = 8 cm
Height (H) = 6 cm
Thickness of the wood (T) = 0.5 cm 

Formula Used: 

External volume of the box:

​$$V_{\text{ext}} = \text{Length} \times \text{Breadth} \times \text{Height}$$​​

Internal dimensions:

Internal length = External length - 2 × Thickness

Internal breadth = External breadth - 2 × Thickness

Internal height = External height - 2 × Thickness

Internal volume of the box:

​$$V_{\text{int}} = \text{Internal length} \times \text{Internal breadth} \times \text{Internal height}$$​​

Volume of wood required:

​$$V_{\text{wood}} = V_{\text{ext}} - V_{\text{int}}$$​​

The internal dimensions of the box will be reduced by the thickness of the wood on each side:
Internal Length = L - 2T = 10 - 2(0.5) = 9 cm
Internal Breadth = B - 2T = 8 - 2(0.5) = 7 cm
Internal Height = H - 2T = 6 - 2(0.5) = 5 cm
External Volume = L $$\times$$​ B $$\times$$​ H = 10 $$\times$$​8 $$\times$$​ 6 = 480 cubic cm
Internal Volume = Internal Length $$\times$$​ Internal Breadth $$\times$$​ Internal Height = 9 $$\times$$​ 7 $$\times$$​ 5 = 315 cubic cm
Volume of Wood = External Volume -  Internal Volume = 480 - 315 = 165 cubic cm