Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 20 feet. Container B has a diameter of 36 feet and a height of 19 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 the empty portion of Container B, to the nearest tenth of a cubic foot?
To find the volume of the empty portion of Container B, we first need to calculate the volume of water transferred from Container A to Container B.
The volume of Container A can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
For Container A:
- Radius (r) = diameter / 2 = 26 feet / 2 = 13 feet
- Height (h) = 20 feet
Volume of Container A = π * (13 feet)^2 * 20 feet ≈ 10678.38 cubic feet
Since Container A is completely emptied into Container B, the volume of water transferred from A to B is equal to the volume of Container A.
Next, we need to find the volume of Container B when it is full of water.
For Container B:
- Radius (r) = diameter / 2 = 36 feet / 2 = 18 feet
- Height (h) = 19 feet
Volume of Container B = π * (18 feet)^2 * 19 feet ≈ 19320.49 cubic feet
After transferring the water from Container A to Container B, the volume of water in Container B is 19320.49 cubic feet - 10678.38 cubic feet = 8642.11 cubic feet.
Therefore, the volume of the empty portion of Container B is approximately 8642.1 cubic feet (to the nearest tenth of a cubic foot).