Question
An empty container weighs 200 grams. The container's total mass is 750 grams when filled with a liquid. If the liquid has a density of 1.1 g/cm³, what is the volume of the liquid in the container?
Answers
GPT-4o mini
To find the volume of the liquid in the container, we can follow these steps:
1. **Calculate the mass of the liquid**:
- The total mass when filled is 750 grams.
- The weight of the empty container is 200 grams.
- Therefore, the mass of the liquid is:
\[
\text{mass of liquid} = \text{total mass} - \text{mass of container} = 750 \text{ g} - 200 \text{ g} = 550 \text{ g}
\]
2. **Use the density to find the volume**:
- We know the density (\( \rho \)) of the liquid is 1.1 g/cm³.
- The formula relating mass (\( m \)), volume (\( V \)), and density is:
\[
\rho = \frac{m}{V}
\]
Rearranging the formula to find volume gives:
\[
V = \frac{m}{\rho}
\]
3. **Plug in the values**:
- Substituting the mass of the liquid and the density into the formula, we get:
\[
V = \frac{550 \text{ g}}{1.1 \text{ g/cm}^3} = 500 \text{ cm}^3
\]
Thus, the volume of the liquid in the container is **500 cm³**.
1. **Calculate the mass of the liquid**:
- The total mass when filled is 750 grams.
- The weight of the empty container is 200 grams.
- Therefore, the mass of the liquid is:
\[
\text{mass of liquid} = \text{total mass} - \text{mass of container} = 750 \text{ g} - 200 \text{ g} = 550 \text{ g}
\]
2. **Use the density to find the volume**:
- We know the density (\( \rho \)) of the liquid is 1.1 g/cm³.
- The formula relating mass (\( m \)), volume (\( V \)), and density is:
\[
\rho = \frac{m}{V}
\]
Rearranging the formula to find volume gives:
\[
V = \frac{m}{\rho}
\]
3. **Plug in the values**:
- Substituting the mass of the liquid and the density into the formula, we get:
\[
V = \frac{550 \text{ g}}{1.1 \text{ g/cm}^3} = 500 \text{ cm}^3
\]
Thus, the volume of the liquid in the container is **500 cm³**.