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