Given:
We are to fit x number of cylindrical kegs in a truck.
Dimensions of the kegs: Diameter 9 inch, height 32 inch.
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }keg:\text{ }\pi r^2h \\ =\text{ }\pi(4.5^2)*32 \\ =\text{ 648}\pi\text{ cubic inches} \end{gathered}[/tex]Volume of the truck: height * length* breadth
= 9*7*53
=3339 cubic ft
= 40068 inches
To find the amount of kegs that can fit, we divide the volume of the truck by the volume of the kegs and round off to a reasonable number.
[tex]\begin{gathered} =\text{ }\frac{40068}{648\pi} \\ =\text{ 16.68216} \\ \approx\text{ 19 kegs} \end{gathered}[/tex]2.) To find the volume of space left-over:
Volume of 19 kegs:
[tex]\begin{gathered} =\text{ 19*648}\pi \\ =\text{ 38679.289 cubic inches} \\ Subtract\text{ this from the full volume of the truck:} \\ 40068\text{ - 38679.289} \\ =\text{ 1388.711 cubic inches of air space left.} \end{gathered}[/tex]