Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 16 feet. Container B has a diameter of 18 feet and a height of 17 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
To find the volume of the empty space inside Container A after the water has been transferred to Container B, we first need to calculate the volume of water that was in Container A.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
For Container A:
r = 22ft/2 = 11ft
h = 16ft
V_A = π(11ft)^2(16ft)
V_A ≈ 6193.19 cubic feet
Now, let's calculate the volume of water that was transferred to Container B:
For Container B:
r = 18ft/2 = 9ft
h = 17ft
V_B = π(9ft)^2(17ft)
V_B ≈ 4312.10 cubic feet
The empty space inside Container A can be calculated by subtracting the volume of water that was transferred to Container B from the original volume of Container A:
Empty space in Container A = V_A - V_B
Empty space in Container A ≈ 6193.19 cubic feet - 4312.10 cubic feet
Empty space in Container A ≈ 1881.09 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 1881.1 cubic feet.