Consider that in sphering a person is secured inside a small, hollow sphere that is surrounded by a larger sphere. The space between the spheres is inflated with air. Let's see a draw of this situation!
We want to find the volume of the inflated space. To do so, we will use the formula for the volume of a sphere.
V= 4/3Ï€ r^3
Here, r represent the radius of the sphere. In our case, the diameter of the larger sphere is equal to 3 meters. Remember that the radius is half of diameter. Then, the radius of the larger sphere is equal to 1.5 meters. We can substitute this value into the above formula to calculate the volume of the larger sphere.
The volume of the larger sphere is 14.1 cubic meters. Now, we will find the volume of the smaller sphere. Notice that the diameter is equal to 2 meters, then the radius is 1 meter. We will substitute r= 1 into the formula for the volume of a sphere.
Now that we have the volume of both spheres, we can calculate the volume for the inflated space. It will be the difference between the volume of larger and smaller sphere.
V=14.1-4.2 → V= 9.9
The volume of the inflated space is about 9.9 cubic meters.
