The external dimensions of a wooden box, open at the top are 54 cm by 30 cm by 16 cm. It is made of wood 2 cm thick. Calculate (i) the capacity of the box (ii) the volume of wood.
Answers
Answer:
External length of the open box = 65 cm
External breadth of the open box = 34 cm
External height of the open box = 25 cm
External volume of the open box = 65 x 34 x 25 cm3 = 55250 cm3
Internal length of open box = 65 – (2 x 2) cm = 61 cm
Internal breadth of a open box = 34 – (2 x 2) cm = 30 cm
Internal height of open box = 25 – 2 cm = 23 cm
Internal volume of open box or capacity of the box = 61 x 30 x 23 cm3 = 42090 cm3
Volume of wood required to make the closed box = 55250 – 42090 cm3 = 13160 cm3
remaining sides area=2(30 X 16+16 X 54)+1620=4308 cm saq.
To find the capacity
to find the inner volume subtract the dimentions by (2*2)=4
therefore capacity= inner volume= 50*36*12= 15600
so volume of wood= outer volume-inner volume
=54*30*16-50*26*12
=24000-15600
=8400cm^3
18200cm³ , 7720 cm³
Step-by-step explanation:
External dimensions
Length 54 cm
Breadth 30 cm
Height 16 Cm
Internal dimensions
Length 54 -(2+2)=50 cm
Breadth 30 -(2+2) =26 cm
Height 16 -2 = 14
As the box is open from top we subtract only the lower wood thickness
Capacity of the box = internal volume
= 50*26*14= 18200 cm³
External volume = 54*30*16
=25920 cm³
Volume of the wood =external volume - internal volume
=25920-18200
=7720cm³