To find the density of the stone, we need to follow a series of steps involving the given measurements. Let's go through the problem step-by-step:
1. Identify the Given Values:
- Mass of the stone: [tex]\( 112 \)[/tex] grams
- Initial volume of water in the graduated cylinder: [tex]\( 50 \)[/tex] cm[tex]\(^3\)[/tex]
- Final volume of water after the stone is fully immersed: [tex]\( 95 \)[/tex] cm[tex]\(^3\)[/tex]
2. Calculate the Volume of the Stone:
- When the stone is immersed in the water, it displaces an amount of water equal to its own volume.
- The volume of the stone is the difference between the final volume and the initial volume of the water.
[tex]\[
\text{Volume of the stone} = \text{Final water volume} - \text{Initial water volume}
\][/tex]
[tex]\[
\text{Volume of the stone} = 95 \text{ cm}^3 - 50 \text{ cm}^3 = 45 \text{ cm}^3
\][/tex]
3. Calculate the Density of the Stone:
- Density (ρ) is defined as mass per unit volume.
- The formula for density is:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
- Using the values we have:
[tex]\[
\text{Density of the stone} = \frac{112 \text{ g}}{45 \text{ cm}^3}
\][/tex]
- Simplifying this fraction:
[tex]\[
\text{Density of the stone} \approx 2.49 \text{ g/cm}^3
\][/tex]
4. Conclusion:
- The volume of the stone is [tex]\( 45 \)[/tex] cm[tex]\(^3\)[/tex].
- The density of the stone is approximately [tex]\( 2.49 \)[/tex] g/cm[tex]\(^3\)[/tex].
By following these steps, we've determined that the stone has a volume of 45 cm³ and a density of approximately 2.49 g/cm³.
