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, we need to calculate the volume of water in Container A and the volume of Container A itself.
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius of the cylinder and h is the height.
For Container A:
Radius = diameter/2 = 18 ft/2 = 9 ft
Volume = π(9 ft)^2(15 ft) ≈ 3819.7 ft^3
Next, we need to find out how much water was in Container A. Since Container A was full, the volume of water in Container A is equal to the volume of Container A itself, which is approximately 3819.7 ft^3.
Now, we need to find the volume of Container B.
For Container B:
Radius = diameter/2 = 24 ft/2 = 12 ft
Volume = π(12 ft)^2(13 ft) ≈ 6109.1 ft^3
After pumping water from Container A to Container B, the volume of water in Container B will be:
Volume of water in Container B = Volume of Container B - Volume of water in Container A
Volume of water in Container B = 6109.1 ft^3 - 3819.7 ft^3 ≈ 2291.4 ft^3
Therefore, the volume of water in Container B, to the nearest tenth of a cubic foot, is approximately 2291.4 ft^3.