Question

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.​

Answer 1

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

Answer 2

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remaining sides area=2(30 X 16+16 X 54)+1620=4308 cm saq.

$\huge {\underline {\underline {\sf {internals \: and \: external}}}}$

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

$\large {\underline {\purple {\fbox{final}}}}$

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