The outside diameter of the igloo is 12 feet. The thickness of each block of ice that was used to construct the igloo is 1.5 feet. Estimate in cubic feet the amount of space of the living area inside the igloo.

The first thing we are going to do for this case is to model the igloo as a hemisphere.

The volume of the hemisphere is:

V = ((4/3) * (pi) * (r ^ 3)) / 2

Where,

r: sphere radio

We have then that the internal diameter is:

di = 12-1.5

di = 10.5 feet

So the radio is:

r = di / 2

r = 10.5 / 2

r = 5.25 feet

Substituting values:

V = ((4/3) * (pi) * ((5.25) ^ 3)) / 2

V = 303.1 feet ^ 3

Answer:

the amount of space of the living area inside the igloo is:

V = 303.1 feet ^ 3