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How many cubic centimeters of iron is required to construct an open box whose external dimensions are $36$ cm, $25$ cm and $16.5$ cm provided the thickness of the iron is $1.5$ cm. If one cubic cm of iron weighs $7.5$ g, then the weight of the box from the following choices is:

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25.7 k g

29.7 k g

32.7 k g

35.7 k g

answer is B.

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Detailed Solution

The external dimensions of an open box are

l = 36

cm,

b = 25

cm,

h = 16.5

cm and thickness is

x = 1.5

cm.
Draw a diagram by assuming thickness of an open box is

x

Obtain the external volume of an open box.
The external dimensions of an open box are l= 36 cm, b = 25cm,

h = 16.5

cm.
So, the volume of the external dimension of a open box is,
Question Image

Obtain the internal dimensions of an open box.
The length of an open box is,

l' = l − 2 x l' = 36 − 2 1.5 l' = 33 cm

The breadth of an open box is,

b ′ = b − 2 x b ′ = 25 − 2 1.5 b ′ = 22 cm

The height of an open box is,

h' = h − 2 x h' = 16 − 2 1.5 h' = 15 cm

The internal volume of an open box become,

V I = l' b' h' V I = 33 × 22 × 15 V I = 10890 cm 3

Obtain the total iron to construct an open box.
We get,
Question Image

Obtain the weight of an open box.
Given that, one cubic cm of iron weighs

7.5

g.
Since, 1000 g = 1 kg,

7.5 g = 7.5 1000 k g

And hence,

w = 7.5 1000 k g

Obtain the weight of an open box.

W = V t × w W = 3960 × 7.5 1000 kg W = 29.7 kg

The weight of the box is 29.7 kg respectively.
Hence, option 2) is correct.

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