Question

a hollow cylindrical metallic pipe is 21 cm long if the external and internal diameter of the pipe are 12cm and 8cm respectively find the volume of metal used in making the pipe​

Answer 1

The volume of the metal used to make the pipe is
`\mathbf{1,680\pi\ cm^3}`

Explanation:

The Volume of a Cylinder

Given a right cylinder of base radius r and height h, the volume is calculated as follows:

`V=\pi r^2h`

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:

`V_e=\pi r_e^2h`

`V_e=\pi 12^2*21`

`V_e=3,024\pi\ cm^3`

Calculating the internal volume:

`V_i=\pi r_i^2h`

`V_i=\pi 8^2*21`

`V_i=1,344\pi\ cm^3`

The volume of metal is:

`V_m=V_e-V_i=3,024\pi\ cm^3-1,344\pi\ cm^3`

`V_m=1,680\pi\ cm^3`

The volume of the metal used to make the pipe is
`\mathbf{1,680\pi\ cm^3}`