Question

How many cubic centimeters of iron are there in an open box whose external dimension are 36 cm, 25 cm, 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cm3 of iron weighs 15g, find the weight of the empty box in kilograms.​

Answer 1

Answer:

External volume (without counting hollow part) = 36*25*16.5 = 14850 cc

Internal dimensions of box:

=> 36-2(1.5) = 33cm

=> 25-2(1.5) = 22cm

=> 16.5-2(1.5) = 13.5cm

Volume of hollow part in box = 33*22*13.5 = 9801 cc

Box is open, therefore top part must be removed.

Volume of top part = 36*25*1.5 = 1350 cc

Therefore, volume of box = 14850-9801-1350 = 3699 cc

Weight of box = 3699*15 = 55485g = 55.485 kg

Step-by-step explanation:

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Answer 2

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Here,

As we know that,

Volume of cuboid

= l × b × h

= length × breadth × height

So,

Volume of a box (External)

= (36 × 25 × 16.5) cm

Also,

Thickness of iron will be :-

= 1.5 cm

Here,

Inner length will be :-

= 36 - 2 × 1.5

= 36 - 3

= 33 cm

Also,

Inner breadth will be :-

= 25 - 2 × 1.5

= 25 - 3

= 23 cm

Also,

Inner height will be :-

= 16.5 - 1.5

= 15 cm

Now,

Inner volume (Box)

= (33 × 22 ×15) cm

Now

V = (External - Internal)Volume

V = (36 × 25 × 16.5) - (33 × 22 × 15)

V = 14850 - 10890

V = 3960 cm³

Volume of iron occupied :-

= 3960 cm³

Here,

1cm³ iron of weight = 15 gm

Therefore,

3960 cm³ iron of weight

= 3960 × 15

= 59400 gm

As we know that :-

1g = 1/1000 kg

= 59400/1000

= 59.4 kg