To determine the correct order of masses from least to greatest, let's go through our calculations step-by-step for each container.
1. Container A (Hydrogen, cube):
- Density: 0.09 mg/cm³
- Side length: 15 cm
The volume of a cube is given by \( \text{Volume} = \text{side}^3 \).
[tex]\[
\text{Volume}_A = 15^3 = 3375 \, \text{cm}^3
\][/tex]
The mass is then calculated by \( \text{Mass} = \text{Density} \times \text{Volume} \).
[tex]\[
\text{Mass}_A = 0.09 \, \text{mg/cm}^3 \times 3375 \, \text{cm}^3 = 303.75 \, \text{mg}
\][/tex]
2. Container B (Helium, rectangular prism):
- Density: 0.175 mg/cm³
- Dimensions: 14 cm, 12 cm, 10 cm
The volume of a rectangular prism is given by \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \).
[tex]\[
\text{Volume}_B = 14 \times 12 \times 10 = 1680 \, \text{cm}^3
\][/tex]
The mass is then calculated by \( \text{Mass} = \text{Density} \times \text{Volume} \).
[tex]\[
\text{Mass}_B = 0.175 \, \text{mg/cm}^3 \times 1680 \, \text{cm}^3 = 294 \, \text{mg}
\][/tex]
3. Container C (Nitrogen, sphere):
- Density: 1.251 mg/cm³
- Diameter: 8 cm
The volume of a sphere is given by \( \text{Volume} = \frac{4}{3} \pi \left( \frac{\text{diameter}}{2} \right)^3 \).
The radius is half of the diameter.
[tex]\[
\text{Radius}_C = \frac{8}{2} = 4 \, \text{cm}
\][/tex]
[tex]\[
\text{Volume}_C = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi \times 64 = \frac{256}{3} \pi \, \text{cm}^3
\][/tex]
The mass is then calculated by \( \text{Mass} = \text{Density} \times \text{Volume} \).
[tex]\[
\text{Mass}_C = 1.251 \, \text{mg/cm}^3 \times \frac{256}{3} \pi \approx 335.37 \, \text{mg}
\][/tex]
Now that we have the masses:
- Mass of A: 303.75 mg
- Mass of B: 294 mg
- Mass of C: 335.37 mg
Arranging these from least to greatest:
[tex]\[
\boxed{B, A, C}
\][/tex]
