Answer
The required volume of the gas is $29\frac{1}{3}\text{ cubic inches}$.
Work Step by Step
Consider the details; the volume of the provided mass of gas varies inversely to the applied pressure. A certain mass of the gas has a volume of $40$ cubic inches at $22$ pounds of pressure.
$V=\frac{k}{P}$
Substitute, $V=40$, and $P=22$.
Solve for $k$.
$\begin{align}
& V=\frac{k}{P} \\
& 40=\frac{k}{22} \\
& k=40\left( 22 \right) \\
& =880
\end{align}$
Now, obtain the volume $V$ at $k=880$ and $P=30$.
$\begin{align}
& V=\frac{880}{30} \\
& =\frac{88}{3} \\
& =29\frac{1}{3}
\end{align}$
Hence, the volume of the gas is $29\frac{1}{3}\text{ cubic inches}$.
