Question

The DVD stack is shown below consists of 100 disks. The diameter of each disk is 120 millimeters, the diameter of the hollow center of the disk is 15 millimeters, and the thickness is 1.2 millimeters. What is the volume of the stack in terms of LaTeX: \pi π ?

Answer 1

The volume of the stack is
`425.250\pi\ mm^(3)`

Explanation:

we know that

The volume of the cylinder (DVD stack) is equal to

`V=Bh`

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

`B=\pi (r2^(2) -r1^(2))`

we have

`r2=120/2=60\ mm` -----> the radius is half the diameter

`r1=15/2=7.5\ mm` -----> the radius is half the diameter

substitute

`B=\pi (60^(2) -7.5^(2))`

`B=3,543.75\pi\ mm^(2))`

Find the height of the stack

`h=100*(1.2)=120\ mm`

Find the volume

`V=(3,543.75\pi)(120)=425.250\pi\ mm^(3)`