The external dimensions of wooden box are $18 cm, 10 cm$ and $6 cm$ respectively and thickness of the wood is $5 mm$ . If the empty box weighs
$3.15 kg$ , the weight of $1 c . c .$ of wood is.

$7 gm$

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$15 gm$

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$10 gm$

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$1 gm$

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Solution

The correct option is C
$10 gm$

Step 1: Given data
External dimensions of wooden box,
$l_{1} = 18 c m b_{1} = 10 c m h_{1} = 6 c m$
The thickness of the wood $= 5 m m = \frac{5}{10} = 0.5 c m$
Weight of one empty box $= 3.15 k g$
Weight of $1 c . c .$ wood=?
Volume of cuboid $= l \times b \times h$
Step 3: Calculating the weight of $1 c . c .$ wood
Internal dimensions of the wooden box will be given as,
$E x t e r n a l d i m e n s i o n s - 2 \times t h i c k n e s s$
Thus, the Internal dimensions of the wooden box,
$l_{2} = 18 - 2 \times 0.5 = 18 - 1 = 17 c m b_{2} = 10 - 1 = 9 c m h_{2} = 6 - 1 = 5 c m$
The volume of wood is given as,
External volume-Internal volume
$= 18 \times 10 \times 6 - 17 \times 9 \times 5 = 1080 - 765 = 315 c . c .$
The volume of wood is equal to the volume of one empty box.
Thus,
$315 c . c . = 3.15 k g = 3.15 \times 1000 g 1 c . c . = \frac{3150}{315} = 10 g$
Hence, the weight of $1 c . c .$ of wood is $10 g$

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The external dimensions of wooden box are 18cm,10cm and 6cm respectively and thickness of the wood is 5mm. If the empty box weighs3.15kg, the weight of 1c.c. of wood is.

The external dimensions of wooden box are $18 cm, 10 cm$ and $6 cm$ respectively and thickness of the wood is $5 mm$ . If the empty box weighs
$3.15 kg$ , the weight of $1 c . c .$ of wood is.