Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 8 feet and a height of 11 feet. Container B has a diameter of 6 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Question
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 8 feet and a height of 11 feet. Container B has a diameter of 6 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Solution
To solve this problem, we need to calculate the volumes of both containers and then determine how much water is left in Container A after Container B is filled.
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Calculate the volume of Container A:
- Diameter of Container A = 8 feet
- Radius of Container A = Diameter / 2 = 8 / 2 = 4 feet
- Height of Container A = 11 feet
- Volume of a cylinder = π * radius² * height
- Volume of Container A = π * (4)² * 11 = π * 16 * 11 = 176π cubic feet
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Calculate the volume of Container B:
- Diameter of Container B = 6 feet
- Radius of Container B = Diameter / 2 = 6 / 2 = 3 feet
- Height of Container B = 18 feet
- Volume of Container B = π * (3)² * 18 = π * 9 * 18 = 162π cubic feet
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Determine the volume of water transferred from Container A to Container B:
- Since Container B is completely filled, the volume of water transferred is equal to the volume of Container B.
- Volume of water transferred = 162π cubic feet
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Calculate the remaining volume of water in Container A:
- Initial volume of water in Container A = 176π cubic feet
- Volume of water transferred to Container B = 162π cubic feet
- Remaining volume of water in Container A = 176π - 162π = 14π cubic feet
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Convert the remaining volume to a numerical value:
- π ≈ 3.14159
- Remaining volume of water in Container A = 14π ≈ 14 * 3.14159 ≈ 43.98226 cubic feet
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Round to the nearest tenth:
- 43.98226 rounded to the nearest tenth is 44.0 cubic feet
Therefore, the volume of the empty space inside Container A, to the nearest tenth of a cubic foot, is 44.0 cubic feet.
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