Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 18 feet and a height of 15 feet. Container B has a diameter of 24 feet and a height of 13 feet.
Container A is full of water and the water is pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tenth of a cubic foot?
First, let's calculate the volume of water in Container A:
Radius of Container A = diameter / 2 = 18 feet / 2 = 9 feet
Volume of Container A = π * (radius)^2 * height
Volume of Container A = π * (9 feet)^2 * 15 feet
Volume of Container A = π * 81 feet^2 * 15 feet
Volume of Container A = 1215π cubic feet
Now, let's calculate the volume of water that was transferred from Container A to Container B:
Radius of Container B = diameter / 2 = 24 feet / 2 = 12 feet
Volume of water transferred = Volume of Container A - Volume of remaining space in Container B
Volume of water transferred = 1215π cubic feet - (π * (12 feet)^2 * 13 feet)
Volume of water transferred = 1215π cubic feet - 561.6π cubic feet
Volume of water transferred = 653.4π cubic feet
Finally, let's find the volume of water in Container B:
Volume of water in Container B = Volume of water transferred + Volume of remaining space in Container B
Volume of water in Container B = 653.4π cubic feet + (π * (12 feet)^2 * 13 feet)
Volume of water in Container B = 653.4π cubic feet + 561.6π cubic feet
Volume of water in Container B = 1215π cubic feet
To find the volume to the nearest tenth of a cubic foot, we can calculate the value of 1215π:
1215π ≈ 3816.8 cubic feet
Therefore, the volume of water in Container B after the pumping is complete is approximately 3816.8 cubic feet.