Answer: 3,893,845.918 Ping-Pong balls
Explanation:
The volume of an average room is:
[tex]V_{room}=(length)(width)(height)[/tex] (1)
[tex]V_{room}=(12 ft)(18 ft)(9 ft)=1944 ft^{3}[/tex] (2)
Now let’s transform this [tex]V_{room}[/tex] to units of [tex]cm^{3}[/tex], knowing [tex]1 ft=30.48 cm[/tex]:
[tex]V_{room}=1944 ft^{3}\frac{{(30.48 cm)}^{3}}{1ft^{3}}=55,047,949.78 cm^{3}[/tex] (3)
On the other hand, we have Ping-Pong balls with a radius [tex]r=1.5 cm[/tex], and their volume is given by:
[tex]V_{balls}=\frac{4}{3} \pi r^{3}[/tex] (4)
[tex]V_{balls}=\frac{4}{3} \pi (1.5 cm)^{3}[/tex] (5)
[tex]V_{balls}=14.137 cm^{3}[/tex] (6)
Now, the number [tex]n[/tex] of Ping-Pong balls that can be packed into the room is:
[tex]n=\frac{V_{room}}{V_{balls}}[/tex] (7)
[tex]n=\frac{55,047,949.78 cm^{3}}{14.137 cm^{3}}[/tex] (8)
[tex]n=3,893,845.918[/tex] This is the number of Ping-Pong balls that can be packed into an average size room
