Answer :
To determine the mass of helium in the blimp, let's follow a series of steps:
1. Conversion of Volume:
- We need to convert the given volume in milliliters to cubic meters. Given, the volume of helium is [tex]\(6.28 \times 10^9 \)[/tex] milliliters.
- We know that [tex]\(1,000 L = 1\)[/tex] cubic meter. Hence, [tex]\(1 \text{ milliL} = 1 \times 10^{-6} \text{ cubic meters}\)[/tex].
- Therefore, [tex]\(6.28 \times 10^9\)[/tex] milliliters is equal to [tex]\(6.28 \times 10^9 \times 10^{-6}\)[/tex] cubic meters.
- Simplifying this, we get:
[tex]\[ 6.28 \times 10^9 \times 10^{-6} = 6.28 \times 10^3 = 6280 \text{ cubic meters} \][/tex]
2. Compute the Mass:
- The density of helium is given as [tex]\(0.1786 \frac{\text{ kilogram}}{\text{ cubic meter }}\)[/tex].
- Mass can be calculated using the formula:
[tex]\[ \text{Mass} = \text{Density} \times \text{Volume} \][/tex]
- Substituting the values we have:
[tex]\[ \text{Mass} = 0.1786 \frac{\text{ kg}}{\text{ m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kilograms} \][/tex]
Comparing the computed mass with the given options, we find:
A. [tex]\(1,120 \text{ kg}\)[/tex] (This is the correct answer considering minor rounding)
B. [tex]\(1.12 \text{ kg}\)[/tex] (Incorrect, too low)
C. [tex]\(3.52 \times 10^7 \text{ kg}\)[/tex] (Incorrect, too high)
D. [tex]\(2,840 \text{ kg}\)[/tex] (Incorrect, too high)
Therefore, the correct answer is:
A. 1,120 kg
1. Conversion of Volume:
- We need to convert the given volume in milliliters to cubic meters. Given, the volume of helium is [tex]\(6.28 \times 10^9 \)[/tex] milliliters.
- We know that [tex]\(1,000 L = 1\)[/tex] cubic meter. Hence, [tex]\(1 \text{ milliL} = 1 \times 10^{-6} \text{ cubic meters}\)[/tex].
- Therefore, [tex]\(6.28 \times 10^9\)[/tex] milliliters is equal to [tex]\(6.28 \times 10^9 \times 10^{-6}\)[/tex] cubic meters.
- Simplifying this, we get:
[tex]\[ 6.28 \times 10^9 \times 10^{-6} = 6.28 \times 10^3 = 6280 \text{ cubic meters} \][/tex]
2. Compute the Mass:
- The density of helium is given as [tex]\(0.1786 \frac{\text{ kilogram}}{\text{ cubic meter }}\)[/tex].
- Mass can be calculated using the formula:
[tex]\[ \text{Mass} = \text{Density} \times \text{Volume} \][/tex]
- Substituting the values we have:
[tex]\[ \text{Mass} = 0.1786 \frac{\text{ kg}}{\text{ m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kilograms} \][/tex]
Comparing the computed mass with the given options, we find:
A. [tex]\(1,120 \text{ kg}\)[/tex] (This is the correct answer considering minor rounding)
B. [tex]\(1.12 \text{ kg}\)[/tex] (Incorrect, too low)
C. [tex]\(3.52 \times 10^7 \text{ kg}\)[/tex] (Incorrect, too high)
D. [tex]\(2,840 \text{ kg}\)[/tex] (Incorrect, too high)
Therefore, the correct answer is:
A. 1,120 kg
