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The volume of helium in a blimp is [tex]$6.28 \times 10^9$[/tex] milliliters. The density of helium in the blimp is [tex]$0.1786 \frac{\text{kilogram}}{\text{meter}^3}$[/tex]. Find the mass of the helium in the blimp. (Hint: [tex]1,000 \, \text{L} = 1[/tex] cubic meter.)

A. [tex]1,120 \, \text{kg}[/tex]
B. [tex]1.12 \, \text{kg}[/tex]
C. [tex]3.52 \times 10^7 \, \text{kg}[/tex]
D. [tex]2,840 \, \text{kg}[/tex]



Answer :

GinnyAnswer
Alright, let's find the mass of helium in the blimp step by step.

1. Convert the volume from milliliters to liters:
The volume of helium given is [tex]\( 6.28 \times 10^9 \)[/tex] milliliters. Recall that:
[tex]\[ 1 \text{ liter} = 1000 \text{ milliliters} \][/tex]
Therefore, to convert the volume from milliliters to liters:
[tex]\[ \frac{6.28 \times 10^9 \text{ milliliters}}{1000} = 6.28 \times 10^6 \text{ liters} \][/tex]

2. Convert the volume from liters to cubic meters:
We know that:
[tex]\[ 1000 \text{ liters} = 1 \text{ cubic meter} \][/tex]
Hence, converting the volume from liters to cubic meters involves dividing by 1000:
[tex]\[ \frac{6.28 \times 10^6 \text{ liters}}{1000} = 6280 \text{ cubic meters} \][/tex]

3. Calculate the mass of helium:
The density of helium is given as [tex]\( 0.1786 \frac{\text{kilogram}}{\text{cubic meter}} \)[/tex]. To find the mass, we use the formula:
[tex]\[ \text{mass} = \text{density} \times \text{volume} \][/tex]
Plugging in the values:
[tex]\[ \text{mass} = 0.1786 \frac{\text{kg}}{\text{m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kg} \][/tex]

Therefore, the correct answer is:
[tex]\[ A. \quad 1121 \text{ kg} \][/tex]

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