To find the volume of a hemisphere, we use the formula for the volume of a hemisphere:
[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the hemisphere,
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the hemisphere.
Given that the radius [tex]\( r \)[/tex] of the igloo's hemisphere is 4.5 meters, let's plug this value into the formula and solve for the volume.
1. Cube the radius:
[tex]\[ r^3 = (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \][/tex]
2. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[ \pi \times 91.125 = 3.14159 \times 91.125 \approx 286.277 \][/tex]
3. Multiply by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[ V = \frac{2}{3} \times 286.277 \approx 190.8517537055799 \][/tex]
So, the volume of the hemisphere is approximately 190.8517537055799 cubic meters.
4. Round the result to the nearest tenth:
The volume rounded to the nearest tenth is approximately 190.9 cubic meters.
Therefore, the volume of the igloo is approximately 190.9 cubic meters.
