Question
A measuring cylinder contains 50 cm ^3 of water. A stone has a mass of 1.75 g the stone is lowered into the cylinder rises to 52.5 cm^3 calculate the density of the stone.
Answers
GPT-4o mini
To calculate the density of the stone, we first need to determine its volume and then use the mass and volume to find the density.
1. **Calculate the volume of the stone:**
- Initially, the volume of water in the cylinder is 50 cm³.
- After the stone is submerged, the volume rises to 52.5 cm³.
- The volume of the stone is the difference in the water level:
\[
\text{Volume of the stone} = 52.5 \, \text{cm}^3 - 50 \, \text{cm}^3 = 2.5 \, \text{cm}^3
\]
2. **Use the mass of the stone:**
- The mass of the stone is given as 1.75 g.
3. **Calculate the density of the stone:**
- Density (\( \rho \)) is defined as mass divided by volume:
\[
\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{1.75 \, \text{g}}{2.5 \, \text{cm}^3}
\]
\[
\text{Density} = 0.7 \, \text{g/cm}^3
\]
Thus, the density of the stone is **0.7 g/cm³**.
1. **Calculate the volume of the stone:**
- Initially, the volume of water in the cylinder is 50 cm³.
- After the stone is submerged, the volume rises to 52.5 cm³.
- The volume of the stone is the difference in the water level:
\[
\text{Volume of the stone} = 52.5 \, \text{cm}^3 - 50 \, \text{cm}^3 = 2.5 \, \text{cm}^3
\]
2. **Use the mass of the stone:**
- The mass of the stone is given as 1.75 g.
3. **Calculate the density of the stone:**
- Density (\( \rho \)) is defined as mass divided by volume:
\[
\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{1.75 \, \text{g}}{2.5 \, \text{cm}^3}
\]
\[
\text{Density} = 0.7 \, \text{g/cm}^3
\]
Thus, the density of the stone is **0.7 g/cm³**.