If two quantities (V , P) are in inverse proportion, so
[tex]\begin{gathered} V=\frac{K}{P} \\ OR \\ \frac{V_1}{V_2}=\frac{P_2}{P_1} \end{gathered}[/tex]You can use one of these two rules to solve your question
K is the constant of variation, you can find it by using the initial values
Let us use the second rule
When V = 270 cubic inches, P = 6 pounds/square inch
We need to find V = ?, P = 7 pounds/square inch
By using the second rule
[tex]\frac{270}{V_2}=\frac{7}{6}[/tex]By using cross multiplication
[tex]\begin{gathered} 7V_2=270\times6 \\ 7V_2=1620 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7V_2}{7}=\frac{1620}{7} \\ V_2=231.429 \end{gathered}[/tex]Round the answer to the nearest integers
[tex]V_2=231inch^3[/tex]The volume of the gas is 231 cubic inches
