Answer :
To determine the volume of 22.5 grams of water, given that the density of water is 1 gram per cubic centimeter (g/cm³), we follow these steps:
1. Understand the Relationship Between Mass, Density, and Volume: The basic formula that relates mass, density, and volume is:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
Here:
- Mass (\(m\)) is the amount of matter in the object, measured in grams (g).
- Density (\(\rho\)) is the mass per unit volume of a substance, measured in grams per cubic centimeter (g/cm³).
- Volume (\(V\)) is the amount of space the object occupies, measured in cubic centimeters (cm³).
2. Identify Given Values:
- Mass of water (\(m\)) = 22.5 grams.
- Density of water (\(\rho\)) = 1 g/cm³.
3. Substitute the Values into the Formula:
[tex]\[ V = \frac{m}{\rho} \][/tex]
Plugging in the known values:
[tex]\[ V = \frac{22.5 \text{ g}}{1 \text{ g/cm}^3} \][/tex]
4. Calculate the Volume:
When we divide 22.5 grams by the density of water (1 g/cm³), the grams (g) cancel out, leaving us with cubic centimeters (cm³):
[tex]\[ V = \frac{22.5 \text{ g}}{1 \text{ g/cm}^3} = 22.5 \text{ cm}^3 \][/tex]
Therefore, the volume of 22.5 grams of water is 22.5 cubic centimeters.
1. Understand the Relationship Between Mass, Density, and Volume: The basic formula that relates mass, density, and volume is:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
Here:
- Mass (\(m\)) is the amount of matter in the object, measured in grams (g).
- Density (\(\rho\)) is the mass per unit volume of a substance, measured in grams per cubic centimeter (g/cm³).
- Volume (\(V\)) is the amount of space the object occupies, measured in cubic centimeters (cm³).
2. Identify Given Values:
- Mass of water (\(m\)) = 22.5 grams.
- Density of water (\(\rho\)) = 1 g/cm³.
3. Substitute the Values into the Formula:
[tex]\[ V = \frac{m}{\rho} \][/tex]
Plugging in the known values:
[tex]\[ V = \frac{22.5 \text{ g}}{1 \text{ g/cm}^3} \][/tex]
4. Calculate the Volume:
When we divide 22.5 grams by the density of water (1 g/cm³), the grams (g) cancel out, leaving us with cubic centimeters (cm³):
[tex]\[ V = \frac{22.5 \text{ g}}{1 \text{ g/cm}^3} = 22.5 \text{ cm}^3 \][/tex]
Therefore, the volume of 22.5 grams of water is 22.5 cubic centimeters.
To find the volume of 22.5 grams of water, you can use the fact that the density of water is approximately 1 gram per milliliter (g/mL) at room temperature.
Given that density (ρ) = mass (m) / volume (V), we can rearrange this to find volume:
\[ V = \frac{m}{ρ} \]
For water, ρ ≈ 1 g/mL, so:
\[ V = \frac{22.5 \text{ g}}{1 \text{ g/mL}} = 22.5 \text{ mL} \]
Therefore, the volume of 22.5 grams of water is 22.5 milliliters.
Given that density (ρ) = mass (m) / volume (V), we can rearrange this to find volume:
\[ V = \frac{m}{ρ} \]
For water, ρ ≈ 1 g/mL, so:
\[ V = \frac{22.5 \text{ g}}{1 \text{ g/mL}} = 22.5 \text{ mL} \]
Therefore, the volume of 22.5 grams of water is 22.5 milliliters.
