16 glass spheres each of radius $ 2 \mathrm{~cm} $ are packed into a cuboidal box of internal dimensions $ 16 \mathrm{~cm} \times 8 \mathrm{~cm} \times 8 \mathrm{~cm} $ and then the box is filled with water. Find the volume of water filled in the box.
Given:
16 glass spheres each of radius \( 2 \mathrm{~cm} \) are packed into a cuboidal box of internal dimensions \( 16 \mathrm{~cm} \times 8 \mathrm{~cm} \times 8 \mathrm{~cm} \) and then the box is filled with water.
To do:
We have to find the volume of water filled in the box.
Solution:
Internal dimensions of the cuboidal box $= 16\ cm \times 8\ cm \times 8\ cm$
This implies,
Volume of the cuboidal box $=16\times8\times8\ cm^3$
$= 1024\ cm^3$
Radius of each glass sphere $= 2\ cm$
Volume of each glass sphere $= \frac{4}{3} \pi r^3$
$= \frac{4}{3} \times \frac{22}{7} \times 2^3$
$= \frac{704}{21}$
$= 33.523\ cm^3$
Volume of 16 glass spheres $= 16 \times 33.523$
$= 536.37\ cm^3$
Volume of water filled in the box $=$ Volume of the cuboidal box $-$ Volume of 16 glass spheres
$= 1024 - 536.37$
$= 487.6\ cm^3$
The volume of water filled in the box is $487.6\ cm^3$.
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