Explanation:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
For Container A, the diameter is 22 feet, so the radius is 11 feet. The height is 16 feet. Therefore, the volume of Container A is:
V_A = π(11 ft)^2 * 16 ft ≈ 6,788.4 cubic feet
For Container B, the diameter is 18 feet, so the radius is 9 feet. The height is 17 feet. Therefore, the volume of Container B is:
V_B = π(9 ft)^2 * 17 ft ≈ 4,829.6 cubic feet
When the water from Container A is pumped into Container B, it will completely fill Container B and raise the water level to a height of h_B in Container A. The volume of the empty space inside Container A after the pumping is complete is equal to the difference between the volume of Container A and the volume of water that was pumped into Container B:
V_empty = V_A - V_water
To find V_water, we need to calculate the volume of water that was pumped out of Container A and into Container B. Since the two containers have the same base area (the circular top), the height of the water in Container A must be equal to the height of the water in Container B. Let h be the height of the water level in both containers after the pumping is complete. Then the volume of water pumped into Container B is:
V_water = π(9 ft)^2 * h
Since Container B is completely full, we know that h = 17 feet. Therefore, the volume of water pumped into Container B is:
V_water = π(9 ft)^2 * 17 ft ≈ 4,829.6 cubic feet
Substituting this value into the equation for V_empty, we get:
V_empty = V_A - V_water ≈ 6,788.4 cubic feet - 4,829.6 cubic feet ≈ 1,958.8 cubic feet
Therefore, the volume of the empty space inside Container A after the pumping is complete is approximately 1,958.8 cubic feet, to the nearest tenth of a cubic foot.