Answer:
[tex]96\ basketballs[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder (hollow drum)
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=48\ in[/tex]
[tex]r=24\ in[/tex]
substitute
[tex]V=\pi (24)^{2} (48)[/tex]
[tex]V=27,648\pi\ in^{3}[/tex]
step 2
Find the volume of one basketball
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=6\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ in^{3}[/tex]
step 3
Find the maximum number of basketballs that the cylindrical drum contains
so
Divide the volume of the cylinder by the volume of one basketball
[tex]27,648\pi/288\pi=96\ basketballs[/tex]
