Question

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.

Answer 1

Explanation:

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).

`V_o-V_i` That's volume outer - volume inner. To find the outer volume:

`V=\pi r^2h` so

`V_o=\pi (4^2)(300)` and

`V_o=4800\pi` and do the same for the inner volume:

`V_i=\pi (2.5^2)(300)` and

`V_i=1875\pi`

Subtract the inner from the outer:

`4800\pi-1875\pi=2925\pi cm^3`

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

9189.16 cm³