Answer
$\dfrac{25}{8} \text{ cubic meters}$
Work Step by Step
The variation model described by the problem is $
P=\dfrac{k}{V}
,$ where $
P
$ is the pressure, and $
V
$ is the volume.
Substituting the known values in the variation model above results to
\begin{array}{l}\require{cancel}
1250=\dfrac{k}{2}
\\
1250(2)=k
\\
k=2500
.\end{array}
Therefore, the variation equation is
\begin{array}{l}\require{cancel}
P=\dfrac{2500}{V}
.\end{array}
Using the variation equation above, then
\begin{array}{l}\require{cancel}
800=\dfrac{2500}{V}
\\
800V=2500
\\
V=\dfrac{2500}{800}
\\
V=\dfrac{\cancel{100}\cdot25}{\cancel{100}\cdot8}
\\
V=\dfrac{25}{8}
.\end{array}
Hence, the volume, $V,$ is $
\dfrac{25}{8} \text{ cubic meters}
.$
