A box with lid is made of 2 cm thick wood. Its external length,
Question:

A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of a fluid can be placed in it? Also, find the volume of the wood used in it.

 

Solution:

Given,

The external dimensions of cuboid are as follows

Length (l) = 25 cm

Breadth (b) = 18 cm

Height (h) = 15 cm

External volume of the case with cover (cuboid) $=1^{*} \mathrm{~b}^{*} \mathrm{~h} \mathrm{~cm}^{3}$

$=25^{*} 18^{*} 15 \mathrm{~cm}^{3}$

$=6750 \mathrm{~cm}^{3}$

Now, the internal dimensions of the cuboid is as follows

Length (l) = 25 – (2 * 2) = 21 cm

Breadth (b) = 18 – (2 * 2) = 14 cm

Height (h) = 15 – (2 * 2) = 11cm

Now, Internal volume of the case with cover (cuboid) $=1^{*} \mathrm{~b}^{*} \mathrm{~h} \mathrm{~cm}^{3}$

$=21 * 14 * 11 \mathrm{~cm}^{3}$

$=3234 \mathrm{~cm}^{3}$

Therefore, Volume of the fluid that can be placed $=3234 \mathrm{~cm}^{3}$

Now, volume of the wood utilized = External volume – Internal volume

$=3516 \mathrm{~cm}^{3}$

 

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