Question

The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 270 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.

Answer 1

If two quantities (V , P) are in inverse proportion, so

`\begin{gathered} V=(K)/(P) \\ OR \\ (V_1)/(V_2)=(P_2)/(P_1) \end{gathered}`

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

`(270)/(V_2)=(7)/(6)`

By using cross multiplication

`\begin{gathered} 7V_2=270*6 \\ 7V_2=1620 \end{gathered}`

Divide both sides by 7

`\begin{gathered} (7V_2)/(7)=(1620)/(7) \\ V_2=231.429 \end{gathered}`

Round the answer to the nearest integers

`V_2=231inch^3`

The volume of the gas is 231 cubic inches