How much material is required to make a pipe that is 300 cm long whose outer diameter is 8 cm with an inner diameter of 5 cm? Show or explain your work.

If you had a solid cylinder, in order to find the amount of material that makes up that solid cylinder, you would find the volume using the radius of 4 (half of the diameter 8). BUT we want to know the volume of the solid with the radius of 4 minus the solid that has a radius of 2.5 (half of the diameter 5).

[tex]V_o-V_i[/tex] That's volume outer - volume inner. To find the outer volume:

[tex]V=\pi r^2h[/tex] so

[tex]V_o=\pi (4^2)(300)[/tex] and

[tex]V_o=4800\pi[/tex] and do the same for the inner volume:

[tex]V_i=\pi (2.5^2)(300)[/tex] and

[tex]V_i=1875\pi[/tex]

Subtract the inner from the outer:

[tex]4800\pi-1875\pi=2925\pi cm^3[/tex]

If you need your answer in decimal form, then the volume is

9189.16 cm³