Answer
$V=628.2\:\mathrm{in}^3$
Work Step by Step
We can write the given statement as a relation:
$V\:\propto\:\frac{1}{P}$
Let's introduce a proportionality constant $\:k\:$ to turn the relation into an equation as:
$V=k\cdot \frac{1}{P}=\frac{k}{P}$
We can find the value of $\:k\:$ when we are given $\:P=14.7\:$ and $\:V=1000.$
$1000=\frac{k}{14.7}$
$\Rightarrow\: k=14700$
So, now our general equation $\:V=\frac{k}{P}\:$ becomes:
$V=\frac{14700}{P}$
When $\:P=23.4,\:$ we have:
$V=\frac{14700}{23.4}$
$\Rightarrow\: V=628.2$
