Question: The volume (V) of a gas varies inversely as the pressure (P) on the gas. If the volume of a gas is 12 ft3 when the pressure is 10 lb/ft2, find the volume (in ft3) of the gas when the pressure is 4 lb/ft2.
1. **State the problem:**
We know that the volume $V$ of a gas varies inversely as the pressure $P$. Given $V=12$ ft$^3$ when $P=10$ lb/ft$^2$, find $V$ when $P=4$ lb/ft$^2$.
2. **Write the formula for inverse variation:**
$$V \propto \frac{1}{P} \implies V = \frac{k}{P}$$
where $k$ is a constant.
3. **Find the constant $k$ using the given values:**
$$12 = \frac{k}{10} \implies k = 12 \times 10 = 120$$
4. **Use $k$ to find the new volume when $P=4$:**
$$V = \frac{120}{4}$$
5. **Simplify the expression:**
$$V = \frac{\cancel{120}}{\cancel{4}} \times \frac{30}{1} = 30$$
6. **Final answer:**
The volume of the gas when the pressure is 4 lb/ft$^2$ is $30$ ft$^3$.