Final answer:
To calculate the mass of oxygen in the breathing bag with a spherical diameter of 42 cm, we can use the formula for the volume of a sphere and the density of oxygen. The volume of the bag can be calculated using the formula (4/3) * π * r^3, where r is the radius of the sphere. Then, we can multiply the volume by the density of oxygen to find the mass of oxygen.
Step-by-step explanation:
To calculate the mass of oxygen in the breathing bag, we need to know the volume of the bag and the density of oxygen. Given that the bag has a spherical diameter of 42 cm, we can calculate its volume using the formula for the volume of a sphere. With the volume of the bag known, we can then multiply it by the density of oxygen to find the mass of oxygen in grams.
First, let's calculate the volume of the bag:
V = (4/3) * π * r^3
Where r is the radius of the sphere, which is half of the diameter.
r = 42 cm / 2 = 21 cm
V = (4/3) * π * (21 cm)^3
Now, let's calculate the mass of oxygen:
Given density of oxygen: 1.610 g/cm³
Mass = Volume * Density
Mass = (4/3) * π * (21 cm)^3 * 1.610 g/cm³
Finally, calculate the numerical value of the mass using the known value of π:
Mass ≈ 4.28 kg