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The external length, breadth and height of a closed rectangular wooden box are $18 cm, 10 cm$ and $6 cm$ respectively and thickness of wood is $1 / 2 cm$ .When the box is empty it weighs $15 kg$ and when filled with sand it weighs $100 kg .$ Find the weight of the cubic cm of wood and cubic cm of sand.

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121 k g

19 kg

115 k g

0.10 k g

112 k g

0.20 k g

125 k g

0.5 k g

answer is A.

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Detailed Solution

Given that, length, breadth and height of the rectangular box is

and

.
The volume of a cube is expressed as,

V = l b h

where l, b and h be the length, width and height of a cube.
Thus, the volume of a rectangular block is,
Question Image

Since, the thickness of the wood is

12

, so the length, breadth and height of the wooden block is,
Question Image

Similarly,
Question Image

And,

Thus, the volume of hollow space in rectangular block is,
Question Image

So, the volume of rectangular wood is,
Question Image

Since the weight of the empty box is

, thus the weight of a cubic cm of wood is,

W = w V s ⇒ W = 15365 ⇒ W = 121

Since the weight of box filled with sand is

w = 100 k g

, so, the weight of a cubic cm of sand is,

W = weight of sand − weight of empty box Volume of hollow space ⇒ W = 100 − 15 765 ⇒ W = 19 k g

Thus, the weight of a cubic cm of wood is

121 k g

and weight of a cubic cm of sand is

19 kg .

Therefore, option (1) is correct.

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