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What is the volume of a hemisphere with a radius of 39.4 ft, rounded to the nearest tenth of a cubic foot?

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Answer :

The volume of a hemisphere with a radius of 39.4 ft is approximately 128209.0 cubic feet, rounded to the nearest tenth. This is calculated using the formula for the volume of a sphere and then dividing by two. This answer uses the radius to perform the necessary calculations for clarity.

To determine the volume of a hemisphere, we first need to use the formula for the volume of a sphere and then take half of that value.

  1. First, calculate the volume of a sphere using the formula: V = (4/3)πr³, where r is the radius.
  2. Substitute the radius (r = 39.4 ft) into the formula: V = (4/3)π(39.4 ft)³.
  3. Simplifying inside the parentheses first: (39.4 ft)³ = 61124.984 ft³.
  4. Next, multiply by π (approximately 3.14159): V ≈ (4/3) × 3.14159 × 61124.984 ft³ ≈ 256418.01 ft³.
  5. Finally, to find the volume of the hemisphere, divide the result by 2: Volume of Hemisphere ≈ 256418.01 ft³ / 2 ≈ 128209.0 ft³.

Therefore, the volume of the hemisphere with a radius of 39.4 ft, rounded to the nearest tenth, is 128209.0 cubic feet.

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