Answer :
Sure, let's go through the steps to calculate the density for each part of the problem:
a. Mass = 365 g, Volume = 358 cm³
1. Use the formula for density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
2. Plug the values into the formula:
[tex]\[ \text{Density} = \frac{365 \, \text{g}}{358 \, \text{cm}^3} \][/tex]
3. Calculate the density:
[tex]\[ \text{Density} \approx 1.020 \, \text{g/cm}^3 \][/tex]
b. Mass = 0.520 lb, Volume = 756 mL (or cm³)
1. First, convert mass from pounds to grams.
[tex]\( 1 \, \text{lb} = 453.59237 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 0.520 \, \text{lb} \times 453.59237 \, \text{g/lb} \][/tex]
2. Calculate the mass in grams:
[tex]\[ \text{Mass} \approx 235.868 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{235.868 \, \text{g}}{756 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 0.312 \, \text{g/cm}^3 \][/tex]
c. Mass = 7.68 kg, Volume = 1080 cm³
1. Convert mass from kilograms to grams.
[tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 7.68 \, \text{kg} \times 1000 \, \text{g/kg} \][/tex]
2. Mass in grams is:
[tex]\[ \text{Mass} = 7680 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{7680 \, \text{g}}{1080 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 7.111 \, \text{g/cm}^3 \][/tex]
d. Mass = 235 mg, Volume = 1.72 mL (or cm³)
1. Convert mass from milligrams to grams.
[tex]\( 1 \, \text{mg} = 0.001 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 235 \, \text{mg} \times 0.001 \, \text{g/mg} \][/tex]
2. Mass in grams is:
[tex]\[ \text{Mass} = 0.235 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{0.235 \, \text{g}}{1.72 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 0.137 \, \text{g/cm}^3 \][/tex]
And there you have it, the densities for each part are approximately:
- a. [tex]\( 1.020 \, \text{g/cm}^3 \)[/tex]
- b. [tex]\( 0.312 \, \text{g/cm}^3 \)[/tex]
- c. [tex]\( 7.111 \, \text{g/cm}^3 \)[/tex]
- d. [tex]\( 0.137 \, \text{g/cm}^3 \)[/tex]
a. Mass = 365 g, Volume = 358 cm³
1. Use the formula for density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
2. Plug the values into the formula:
[tex]\[ \text{Density} = \frac{365 \, \text{g}}{358 \, \text{cm}^3} \][/tex]
3. Calculate the density:
[tex]\[ \text{Density} \approx 1.020 \, \text{g/cm}^3 \][/tex]
b. Mass = 0.520 lb, Volume = 756 mL (or cm³)
1. First, convert mass from pounds to grams.
[tex]\( 1 \, \text{lb} = 453.59237 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 0.520 \, \text{lb} \times 453.59237 \, \text{g/lb} \][/tex]
2. Calculate the mass in grams:
[tex]\[ \text{Mass} \approx 235.868 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{235.868 \, \text{g}}{756 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 0.312 \, \text{g/cm}^3 \][/tex]
c. Mass = 7.68 kg, Volume = 1080 cm³
1. Convert mass from kilograms to grams.
[tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 7.68 \, \text{kg} \times 1000 \, \text{g/kg} \][/tex]
2. Mass in grams is:
[tex]\[ \text{Mass} = 7680 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{7680 \, \text{g}}{1080 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 7.111 \, \text{g/cm}^3 \][/tex]
d. Mass = 235 mg, Volume = 1.72 mL (or cm³)
1. Convert mass from milligrams to grams.
[tex]\( 1 \, \text{mg} = 0.001 \, \text{g} \)[/tex]
[tex]\[ \text{Mass in grams} = 235 \, \text{mg} \times 0.001 \, \text{g/mg} \][/tex]
2. Mass in grams is:
[tex]\[ \text{Mass} = 0.235 \, \text{g} \][/tex]
3. Use the formula for density:
[tex]\[ \text{Density} = \frac{0.235 \, \text{g}}{1.72 \, \text{cm}^3} \][/tex]
4. Calculate the density:
[tex]\[ \text{Density} \approx 0.137 \, \text{g/cm}^3 \][/tex]
And there you have it, the densities for each part are approximately:
- a. [tex]\( 1.020 \, \text{g/cm}^3 \)[/tex]
- b. [tex]\( 0.312 \, \text{g/cm}^3 \)[/tex]
- c. [tex]\( 7.111 \, \text{g/cm}^3 \)[/tex]
- d. [tex]\( 0.137 \, \text{g/cm}^3 \)[/tex]
