The living area inside would be 190.755 ft³.
We find the volume inside the hemisphere. The volume of a sphere is given by the formula
V = (4/3)πr³
Since this is a hemisphere, it is half of the volume:
V = 1/2(4/3)πr³ = 4/6πr³ = 2/3πr³
The diameter of the hemisphere is 12 ft. However, there is 1.5 ft on each side that is a solid block of ice and not living space:
12 - 2(1.5) = 12-3 = 9 ft for the diameter.
The radius is half of the diameter:
9/2 = 4.5
Using this, we have
V = 2/3πr³ = 2/3(3.14)(4.5)³ = 190.755 ft³
