To find the mass of helium in the blimp, we need to follow a series of steps that involve the conversion of units and the application of the formula for mass. Here’s a detailed breakdown of the solution:
1. Convert Volume from Milliliters to Cubic Meters:
- The given volume of helium is [tex]\(6.28 \times 10^9\)[/tex] milliliters.
- We know that [tex]\(1\)[/tex] liter is equivalent to [tex]\(1000\)[/tex] milliliters, and [tex]\(1\)[/tex] cubic meter is equivalent to [tex]\(1000\)[/tex] liters.
- Thus, to convert milliliters to cubic meters, we use the conversion factor [tex]\(1 \text{ cubic meter} = 1000 \text{ liters} = 1,000,000 \text{ milliliters}\)[/tex].
So, we calculate the volume in cubic meters as follows:
[tex]\[
\text{Volume in cubic meters} = \frac{6.28 \times 10^9 \text{ milliliters}}{1,000,000} = 6280 \text{ cubic meters}
\][/tex]
2. Calculate the Mass of Helium:
- The density of helium given is [tex]\(0.1786 \text{ kilograms per cubic meter}\)[/tex].
- Mass is determined by multiplying the volume by the density:
[tex]\[
\text{Mass} = \text{Volume} \times \text{Density}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Mass} = 6280 \text{ cubic meters} \times 0.1786 \text{ kilograms per cubic meter} = 1121.608 \text{ kilograms}
\][/tex]
Thus, the mass of the helium in the blimp is approximately [tex]\(1121.608\)[/tex] kilograms.
Among the provided options, the one that most closely matches this value is:
A. [tex]\(1,120 \text{ kilograms}\)[/tex]
So, the correct answer is [tex]\( \boxed{1,120 \text{ kilograms}} \)[/tex].
