Sure, let's go through the problem step-by-step to find the density of helium in the balloon.
1. Understand the Problem:
- We are given the volume of the weather balloon is [tex]\( 2.2 \times 10^3 \)[/tex] liters.
- We are given the mass of the helium in the balloon is 374 grams.
- We need to find the density of helium in grams per liter.
2. Recall the Formula for Density:
- The density [tex]\(\rho\)[/tex] of a substance is given by the formula:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
- where the mass is in grams and the volume is in liters.
3. Identify the Given Values:
- Mass [tex]\(m\)[/tex]: 374 grams
- Volume [tex]\(V\)[/tex]: [tex]\(2.2 \times 10^3\)[/tex] liters
4. Calculate the Density:
- Substitute the given mass and volume into the formula for density:
[tex]\[
\rho = \frac{374 \text{ grams}}{2.2 \times 10^3 \text{ liters}}
\][/tex]
5. Simplify the Calculation:
- Perform the division:
[tex]\[
\rho = \frac{374}{2200}
\][/tex]
6. Result:
- The density of helium in the balloon is 0.17 grams per liter.
So, the density of helium in the weather balloon is [tex]\(0.17 \text{ grams per liter}\)[/tex].
