An open wooden box 80 cm long,65cm wide, and 45cm high, is made of 2.5 cm thick wood. 1) find the capacity of the box 2) find the volume of wood used 3) weight of box. It is given that 100cm³ of wood weighs 8g?

1 Answer
MJ
Jan 6, 2018

1) #191250 cm^3#
2) #42750 cm^3#
3) #3420g#

Explanation:

Outer dimensions of box (#lxxwxxh#) = #80cmxx65cmxx45 cm#

Thickness of wood = #2.5cm#

Therefore, internal dimensions of box = #(80-2.5xx2)xx(65-2.5xx2)xx(45-2.5)# = #75cmxx60cmxx42.5cm#

Note that the thickness of wood has been subtracted twice from length and width but once from height. That is because the length and width have 2 sides whereas the height has only 1 only one side with the thickness of wood at the base only.

So, capacity of the box = #75cmxx60cmxx42.5cm# =#191250 cm^3#

Volume of wood used = Outer volume of box - inner volume of box

Now, outer volume of box = #80cmxx65cmxx45 cm# = #234000 cm^3#

Therefore, volume of wood used = #234000 cm^3 -191250 cm^3# = #42750cm^3#

It is also given that #100cm^3#of wood weighs = #8g#
Therefore, weight of box = #8/100xx42750# = #3420g#

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