Question

a hollow cylindrical iron pipe with external and internal radii 8cm and 6cm respectively and length 35 cm is melted and recast into a solid wire of thickness 2.8 cm .find the length of wire.

Answer 1

`500\ cm`

Explanation:

step 1

Find the volume of hollow cylinder

`V=\pi (r2^(2)-r1^(2))h`

we have

`r2=8\ cm`

`r1=6\ cm`

`h=35\ cm`

substitute

`V=\pi (8^(2)-6^(2))(35)`

`V=\pi (28)(35)`

`V=980\pi\ cm^(3)`

step 2

we know that

The wire is a solid cylinder with the same volume of the hollow cylinder

so

`V=\pi r^(2)h`

we have

`V=980\pi\ cm^(3)`

`r=2.8/2=1.4\ cm` ----> the radius is half the diameter (thickness)

substitute and solve for h

`980\pi=\pi (1.4)^(2)h`

`980=(1.96)h`

`h=980/(1.96)=500\ cm`