Answer :
To solve the problem of finding the mass of helium in the blimp, we need to follow a series of steps involving unit conversions and applying the formula for mass. Here is the detailed solution:
1. Convert the volume from milliliters to cubic meters:
- We know the volume of helium is \(6.28 \times 10^9\) milliliters.
- To convert milliliters to cubic meters, we use the fact that \(1,000,000\) milliliters \( = 1 \) cubic meter.
- Therefore, the volume in cubic meters is:
[tex]\[ \frac{6.28 \times 10^9 \text{ milliliters}}{1,000,000} = 6280 \text{ cubic meters} \][/tex]
2. Compute the mass using the density:
- The density of helium is given as \(0.1786 \frac{\text{kilogram}}{\text{cubic meter}}\).
- We use the formula for mass:
[tex]\[ \text{mass} = \text{density} \times \text{volume} \][/tex]
- Substituting the given values:
[tex]\[ \text{mass} = 0.1786 \frac{\text{kg}}{\text{m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kg} \][/tex]
Therefore, the mass of the helium in the blimp is \(1121.608\) kilograms.
Looking at the provided options:
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]
The closest and most accurate answer is:
A. [tex]$1,120 \text{ kg}$[/tex]
1. Convert the volume from milliliters to cubic meters:
- We know the volume of helium is \(6.28 \times 10^9\) milliliters.
- To convert milliliters to cubic meters, we use the fact that \(1,000,000\) milliliters \( = 1 \) cubic meter.
- Therefore, the volume in cubic meters is:
[tex]\[ \frac{6.28 \times 10^9 \text{ milliliters}}{1,000,000} = 6280 \text{ cubic meters} \][/tex]
2. Compute the mass using the density:
- The density of helium is given as \(0.1786 \frac{\text{kilogram}}{\text{cubic meter}}\).
- We use the formula for mass:
[tex]\[ \text{mass} = \text{density} \times \text{volume} \][/tex]
- Substituting the given values:
[tex]\[ \text{mass} = 0.1786 \frac{\text{kg}}{\text{m}^3} \times 6280 \text{ m}^3 = 1121.608 \text{ kg} \][/tex]
Therefore, the mass of the helium in the blimp is \(1121.608\) kilograms.
Looking at the provided options:
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]
The closest and most accurate answer is:
A. [tex]$1,120 \text{ kg}$[/tex]
