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 16 feet. Container B has a diameter of 12 feet and a height of 20 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, we need to calculate the volume of water in each container.
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius of the circular base and h is the height of the cylinder.
For Container A:
Radius (r) = diameter/2 = 18 feet/2 = 9 feet
Height (h) = 16 feet
V(A) = π(9)^2(16)
V(A) = 1296π cubic feet
For Container B:
Radius (r) = diameter/2 = 12 feet/2 = 6 feet
Height (h) = 20 feet
V(B) = π(6)^2(20)
V(B) = 720π cubic feet
Next, we find the volume of water transferred from Container A to Container B:
Water transferred = V(A) - V(B)
Water transferred = 1296π - 720π
Water transferred = 576π cubic feet
Finally, we calculate the volume of empty space inside Container A after the transfer:
Empty space in A = V(A) - Water transferred
Empty space in A = 1296π - 576π
Empty space in A = 720π cubic feet
Rounding to the nearest tenth, the volume of the empty space inside Container A is approximately 2261.9 cubic feet.