Question

an open wooden box 80 cm long , 65 cm wide and 45 cm high, is made of 2.5 cm thick wood . find (1) capacity of the box ,(2) volume of wood usedb (3) weightbof the box it being given that 100cm^3 of wood weight 8g​

Answer 1

Step-by-step explanation:

Outer dimensions of box (

l

×

w

×

h

) =

80

c

m

×

65

c

m

×

45

c

m

Thickness of wood =

2.5

c

m

Therefore, internal dimensions of box =

(

80

−

2.5

×

2

)

×

(

65

−

2.5

×

2

)

×

(

45

−

2.5

)

=

75

c

m

×

60

c

m

×

42.5

c

m

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 =

75

c

m

×

60

c

m

×

42.5

c

m

=

191250

c

m

3

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

Now, outer volume of box =

80

c

m

×

65

c

m

×

45

c

m

=

234000

c

m

3

Therefore, volume of wood used =

234000

c

m

3

−

191250

c

m

3

=

42750

c

m

3

box =

8

100

×

42750

=

3420

g

It is also given that

100

c

m

3

of wood weighs =

8

g

Therefore, weight of box =

8

1