Answer:
The volume of the stack is [tex]425.250\pi\ mm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder (DVD stack) is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the stack
Find the area of the base B
The area of the base B is equal to the area of the larger circle minus the area of the hollow center
[tex]B=\pi (r2^{2} -r1^{2})[/tex]
we have
[tex]r2=120/2=60\ mm[/tex] -----> the radius is half the diameter
[tex]r1=15/2=7.5\ mm[/tex] -----> the radius is half the diameter
substitute
[tex]B=\pi (60^{2} -7.5^{2})[/tex]
[tex]B=3,543.75\pi\ mm^{2})[/tex]
Find the height of the stack
[tex]h=100*(1.2)=120\ mm[/tex]
Find the volume
[tex]V=(3,543.75\pi)(120)=425.250\pi\ mm^{3}[/tex]
