Question

The volume of gas in a container at a constant temperature varies inversely as the pressure. If the volume is 32 cubic centimeters at a

pressure of 8 pounds, find the pressure when the volume is 60 cubic centimeters.
The pressure is____
pounds

Answer 1

4.2667 pounds.

Explanation:

To solve this problem, as the measures are inversely proportional, we can use an inverse rule of three (that is, we multiply the lines instead of dividing). So, for the volume of 32 cm3, we have a pressure of 8 pounds, so for a volume of 60 cm3, we have that:

32 cm3 -> 8 pounds

60 cm3 -> x pounds

32 * 8 = 60 * x

x = 32 * 8 / 60 = 4.2667 pounds.

Answer 2

The new pressure is 4.27 pounds

Explanation:

In this question, we have the volume varying inversely as the pressure;

Firstly, let's say the volume is V and the pressure is P

Mathematically;

V ∝ 1/P

Let us insert a constant of proportionality K

⇒ VP = K

Let's calculate the value of K

K = 32
`cm^(3)` × 8 = 256
`cm^(3) pounds`

Now in the second scenario, pressure is unknown but we know the volume to be 60
`cm^(3)`

Recalling; VP = K

P = K/V = 256
`cm^(3) pounds`/60
`cm^(3)` = 4.27 pounds