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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 the 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. The weight of a cubic cm of wood and a cubic cm of sand are respectively:

(a) \(\frac 17\)kg, \(\frac 19\)kg

(b) \(\frac 1{21} \)kg, \(\frac 19\)kg

(c) \(\frac 1{21} \)kg, \(\frac 17\)kg

(d) \(\frac 1{9} \)kg, \(\frac 17\)kg

1 Answer

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Correct option is (b) \(\frac 1{21} \)kg, \(\frac 19\)kg

Dimension of a closed rectangular wooden box are 18cm,10cm and 6cm, respectively.

The thickness of wood is 21​cm

∴ Volume of rectangular wooden block = 18 × 10 × 6 = 1080 cm3

And, volume of hollow space in rectangular wooden block = 17 × 9 × 5 = 765 cm3

∴ Volume of rectangular wood = (1080 − 765)cm3 = 365 cm3

Now, weight of empty box = 15kg

∴ Weight of a cubic cm of wood = \(\frac{15}{365}\) = \(\frac 1{21}\) ​kg

Weight of box filled with sand = 100kg

Weight of sand = (100 − 15)kg = 85kg

∴ Weight of a cubic cm of sand = \(\frac{85}{765}\) kg = \(\frac 19\)kg

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