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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{kilograms}}{\text{meter}^3}[/tex]. Find the mass of the helium in the blimp. (Hint: [tex]1,000 \text{ L} = 1 \text{ cubic meter}[/tex].)

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
To determine the mass of helium in the blimp, we need to first convert the volume of helium from milliliters to cubic meters and then use the given density to find the mass. Let's follow these steps:

1. Convert the volume from milliliters to cubic meters:
- Given volume: [tex]\(6.28 \times 10^9\)[/tex] milliliters
- Conversion factor: [tex]\(1 \text{ milliliter} = 1 \times 10^{-6} \text{ cubic meters}\)[/tex]
- So, the volume in cubic meters:
[tex]\[ \text{Volume}_{\text{m}^3} = 6.28 \times 10^9 \text{ mL} \times 1 \times 10^{-6} \left( \frac{\text{m}^3}{\text{mL}} \right) = 6280 \text{ m}^3 \][/tex]

2. Calculate the mass of helium:
- Given: Density of helium [tex]\(\rho = 0.1786 \frac{\text{kg}}{\text{m}^3}\)[/tex]
- Volume in cubic meters: [tex]\(6280 \text{ m}^3\)[/tex]
- Use the formula for mass [tex]\( \text{mass} = \text{density} \times \text{volume} \)[/tex]:
[tex]\[ \text{mass}_{\text{helium}} = 0.1786 \frac{\text{kg}}{\text{m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kg} \][/tex]

The mass of the helium in the blimp is approximately 1121.608 kg. The closest answer among the given options is:

A. [tex]\(1,120 \text{ kg}\)[/tex]

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