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Answer :
To find the volume of a hemisphere, you can use the formula:
[tex]\[ V = \frac{2}{3} \times \pi \times r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\(\pi\)[/tex] is a constant (approximately 3.14159), and [tex]\( r \)[/tex] is the radius of the hemisphere.
Let's solve this step by step for a hemisphere with a radius of 39.4 ft:
1. Find the cube of the radius ([tex]\( r^3 \)[/tex]):
[tex]\[ r^3 = 39.4^3 \][/tex]
Calculating [tex]\( 39.4^3 \)[/tex] gives you approximately [tex]\( 612220.984 \)[/tex].
2. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[\pi \times r^3 = \pi \times 612220.984 \approx 192149.181884 \][/tex]
3. Calculate [tex]\(\frac{2}{3}\)[/tex] of the previous result:
[tex]\[ V = \frac{2}{3} \times 192149.181884 \approx 128099.45413735336 \][/tex]
4. Round the volume to the nearest tenth of a cubic foot:
The volume rounded to the nearest tenth is approximately [tex]\( 128099.5 \, \text{ft}^3 \)[/tex].
Therefore, the volume of the hemisphere with a radius of 39.4 ft is approximately [tex]\( 128099.5 \, \text{cubic feet} \)[/tex].
[tex]\[ V = \frac{2}{3} \times \pi \times r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\(\pi\)[/tex] is a constant (approximately 3.14159), and [tex]\( r \)[/tex] is the radius of the hemisphere.
Let's solve this step by step for a hemisphere with a radius of 39.4 ft:
1. Find the cube of the radius ([tex]\( r^3 \)[/tex]):
[tex]\[ r^3 = 39.4^3 \][/tex]
Calculating [tex]\( 39.4^3 \)[/tex] gives you approximately [tex]\( 612220.984 \)[/tex].
2. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[\pi \times r^3 = \pi \times 612220.984 \approx 192149.181884 \][/tex]
3. Calculate [tex]\(\frac{2}{3}\)[/tex] of the previous result:
[tex]\[ V = \frac{2}{3} \times 192149.181884 \approx 128099.45413735336 \][/tex]
4. Round the volume to the nearest tenth of a cubic foot:
The volume rounded to the nearest tenth is approximately [tex]\( 128099.5 \, \text{ft}^3 \)[/tex].
Therefore, the volume of the hemisphere with a radius of 39.4 ft is approximately [tex]\( 128099.5 \, \text{cubic feet} \)[/tex].
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