1.

An open wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5 cm thick wood. Find (i) the capacity of the box, (ii) volume of wood used and (iii) weight of the box, it being givne that 100 `cm^(3)` of wood weight 8g

Answer» External length of the box = 80 cm
External breadth of the box = 65 cm
External height of the box = 45 cm
External volume of the box = `(80 xx 65 xx 45)` cu cm
`= 234000 cm^(3)`
Internal length of the box `= [80 - (2.5 xx 2)] cm = (80 -5)cm`
= 75 cm
Internal breadth of the box `= [65 - (2.5 xx 2)] cm = (65-5) cm`
= 60 cm
Internal height of the box `== (45 - 2.5) cm = 42.5 cm`
(i) Capacity of the box = internal volume of the box
`= (75 xx 60 xx 42.5) cm^(3) = 191250 cm^(3)`
(ii) Volume of wood used
= (external volume) - (internal volume)
`= (234000 - 191250) cm^(3) = 42750 cm^(3)`
Weight of `100 cm^(3)` of wood = 8g
Weight of `42750 cm^(3)` of wood `= ((8)/(100) xx 42750) g = 3420 g`
= 3 kg 420 g


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