Given,

The interior range $$ \[r\text{ }=\text{ }3\text{ }cm\]

What’s more, outside sweep \[R\text{ }=\text{ }r\text{ }+\text{ }r\text{ }=3.0005\text{ }cm\]

\[r\text{ }=\text{ }3.0005\text{ }\text{ }3\text{ }=\text{ }0.0005\text{ }cm\]

Let \[y\text{ }=\text{ }r3\Rightarrow y\text{ }+\text{ }y\text{ }=\text{ }\left( r\text{ }+\text{ }r \right)3\text{ }=\text{ }R3\text{ }=\text{ }\left( 3.0005 \right)3\]

Separating the two sides w.r.t., r, we get

Consequently, the inexact volume of the metal in the shell is \[0.018\pi \text{ }cm3\]