Answer:
The volume of the metal used to make the pipe is [tex]\mathbf{1,680\pi\ cm^3}[/tex]
Step-by-step explanation:
The Volume of a Cylinder
Given a right cylinder of base radius r and height h, the volume is calculated as follows:
[tex]V=\pi r^2h[/tex]
We are given the dimensions of a cylindrical metallic pipe whose external diameter is de=12 cm and the internal diameter is di=8 cm. The height is h=21 cm.
The volume of the metal used in making the pipe is the difference between the external volume and the internal volume.
Calculating the external volume:
[tex]V_e=\pi r_e^2h[/tex]
[tex]V_e=\pi 12^2*21[/tex]
[tex]V_e=3,024\pi\ cm^3[/tex]
Calculating the internal volume:
[tex]V_i=\pi r_i^2h[/tex]
[tex]V_i=\pi 8^2*21[/tex]
[tex]V_i=1,344\pi\ cm^3[/tex]
The volume of metal is:
[tex]V_m=V_e-V_i=3,024\pi\ cm^3-1,344\pi\ cm^3[/tex]
[tex]V_m=1,680\pi\ cm^3[/tex]
The volume of the metal used to make the pipe is [tex]\mathbf{1,680\pi\ cm^3}[/tex]
