Answer :
Let's solve the problem step-by-step based on the information provided:
### Given:
1. Mass of the empty bottle = [tex]\(20 \, \text{g}\)[/tex]
2. Mass of the bottle when full of water = [tex]\(70 \, \text{g}\)[/tex]
3. Mass of the bottle when full of another liquid = [tex]\(55 \, \text{g}\)[/tex]
4. Density of water = [tex]\(1 \, \text{g/cm}^3\)[/tex]
### Calculations:
#### (a) Mass of the water in the bottle
To find the mass of the water alone, we subtract the mass of the empty bottle from the mass of the bottle when it is full of water:
[tex]\[ \text{Mass of the water} = \text{Mass of the full bottle with water} - \text{Mass of the empty bottle} \][/tex]
[tex]\[ \text{Mass of the water} = 70 \, \text{g} - 20 \, \text{g} \][/tex]
[tex]\[ \text{Mass of the water} = 50 \, \text{g} \][/tex]
#### (b) Mass of the liquid in the bottle
Similarly, to find the mass of the second liquid alone, we subtract the mass of the empty bottle from the mass of the bottle when it is full of that liquid:
[tex]\[ \text{Mass of the second liquid} = \text{Mass of the full bottle with the second liquid} - \text{Mass of the empty bottle} \][/tex]
[tex]\[ \text{Mass of the second liquid} = 55 \, \text{g} - 20 \, \text{g} \][/tex]
[tex]\[ \text{Mass of the second liquid} = 35 \, \text{g} \][/tex]
#### (c) Volume of water in the bottle
To find the volume of the water, we use the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Since the density of water is [tex]\(1 \, \text{g/cm}^3\)[/tex], we can rearrange the formula to solve for volume:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
[tex]\[ \text{Volume of water} = \frac{50 \, \text{g}}{1 \, \text{g/cm}^3} \][/tex]
[tex]\[ \text{Volume of water} = 50 \, \text{cm}^3 \][/tex]
### Answers:
(a) Mass of the water: [tex]\(50 \, \text{g}\)[/tex]
(b) Mass of the second liquid: [tex]\(35 \, \text{g}\)[/tex]
(c) Volume of the water: [tex]\(50 \, \text{cm}^3\)[/tex]
### Given:
1. Mass of the empty bottle = [tex]\(20 \, \text{g}\)[/tex]
2. Mass of the bottle when full of water = [tex]\(70 \, \text{g}\)[/tex]
3. Mass of the bottle when full of another liquid = [tex]\(55 \, \text{g}\)[/tex]
4. Density of water = [tex]\(1 \, \text{g/cm}^3\)[/tex]
### Calculations:
#### (a) Mass of the water in the bottle
To find the mass of the water alone, we subtract the mass of the empty bottle from the mass of the bottle when it is full of water:
[tex]\[ \text{Mass of the water} = \text{Mass of the full bottle with water} - \text{Mass of the empty bottle} \][/tex]
[tex]\[ \text{Mass of the water} = 70 \, \text{g} - 20 \, \text{g} \][/tex]
[tex]\[ \text{Mass of the water} = 50 \, \text{g} \][/tex]
#### (b) Mass of the liquid in the bottle
Similarly, to find the mass of the second liquid alone, we subtract the mass of the empty bottle from the mass of the bottle when it is full of that liquid:
[tex]\[ \text{Mass of the second liquid} = \text{Mass of the full bottle with the second liquid} - \text{Mass of the empty bottle} \][/tex]
[tex]\[ \text{Mass of the second liquid} = 55 \, \text{g} - 20 \, \text{g} \][/tex]
[tex]\[ \text{Mass of the second liquid} = 35 \, \text{g} \][/tex]
#### (c) Volume of water in the bottle
To find the volume of the water, we use the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Since the density of water is [tex]\(1 \, \text{g/cm}^3\)[/tex], we can rearrange the formula to solve for volume:
[tex]\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \][/tex]
[tex]\[ \text{Volume of water} = \frac{50 \, \text{g}}{1 \, \text{g/cm}^3} \][/tex]
[tex]\[ \text{Volume of water} = 50 \, \text{cm}^3 \][/tex]
### Answers:
(a) Mass of the water: [tex]\(50 \, \text{g}\)[/tex]
(b) Mass of the second liquid: [tex]\(35 \, \text{g}\)[/tex]
(c) Volume of the water: [tex]\(50 \, \text{cm}^3\)[/tex]
