an open rectangular box has external dimensions as follows: 100cm long,90cm wide and 80cm deep if it is made from wood 2cm thick, calculate the volume of wood in the box
(100)(90)(80) - (100-4)(90-4)(80-4)
To calculate the volume of the wood in the box, we need to find the difference between the outer dimensions and the inner dimensions (taking into account the thickness of the wood).
1. Determine the inner dimensions of the box:
Inner Length = Outer Length - 2 x Wood Thickness
= 100 cm - 2 x 2 cm
= 100 cm - 4 cm
= 96 cm
Inner Width = Outer Width - 2 x Wood Thickness
= 90 cm - 2 x 2 cm
= 90 cm - 4 cm
= 86 cm
Inner Depth = Outer Depth - 2 x Wood Thickness
= 80 cm - 2 x 2 cm
= 80 cm - 4 cm
= 76 cm
2. Calculate the volume of the wood by finding the difference between the outer volume and the inner volume:
Outer Volume = Outer Length x Outer Width x Outer Depth
= 100 cm x 90 cm x 80 cm
= 720,000 cm^3
Inner Volume = Inner Length x Inner Width x Inner Depth
= 96 cm x 86 cm x 76 cm
= 657,216 cm^3
Volume of the Wood = Outer Volume - Inner Volume
= 720,000 cm^3 - 657,216 cm^3
= 62,784 cm^3
Therefore, the volume of the wood in the box is 62,784 cm^3.