Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 8 feet. Container B has a diameter of 8 feet and a height of 18 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?
First, let's calculate the volume of water 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 with a diameter of 16 feet, the radius (r) is half of the diameter, so r = 16/2 = 8 feet. The height (h) is 8 feet.
V(A) = π(8)^2(8) = 512π cubic feet
Next, let's calculate the volume of water that was transferred from Container A to Container B.
For Container B with a diameter of 8 feet, the radius (r) is 4 feet. The height (h) is 18 feet.
V(B) = π(4)^2(18) = 288π cubic feet
Now, let's subtract the volume of water transferred to Container B from the initial volume of water in Container A to find the volume of the empty space inside Container A.
Empty space in Container A = V(A) - V(B) = 512π - 288π = 224π ≈ 704.5 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 704.5 cubic feet.