Final answer:
The volume of the igloo modeled as a hemisphere with a radius of 5.9 meters is approximately 431.1 cubic meters after applying the sphere's volume formula and taking half of the result.
Step-by-step explanation:
To find the volume of an igloo that can be modeled as a hemisphere, we need to use the volume formula for a sphere, which is V = (4/3)πr³, and then divide the result by two, because a hemisphere is half a sphere. Given that the radius (r) of the igloo is 5.9 meters, we substitute this value into the volume formula of the sphere as follows:
V = (4/3)π(5.9 m)³
≈ (4/3)π(205.379 m³)
≈ 862.145 m³
Since the igloo is half a sphere, we then take half of this volume:
V = 862.145 m³ / 2
≈ 431.0725 m³
Rounded to the nearest tenth, the volume of the igloo is 431.1 cubic meters.