Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and a height of 15 feet. Container B has a radius of 7 feet and a height of 9 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 water in Container B, to the nearest tenth of a cubic foot?
To find the volume of water in Container B after transferring the water from Container A, we first need to calculate the volume of water in Container A.
The formula to find the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
For Container A:
V_A = π(4^2)(15)
V_A = π(16)(15)
V_A = 240π
Now, we need to find the volume of Container B. Since the water from Container A was transferred into Container B, the total volume of water in Container B is the sum of the volume of water in Container A and the volume of water still needed to fill Container B.
The volume of Container B can be calculated as follows:
V_B = V_A + π(7^2)(9)
V_B = 240π + π(49)(9)
V_B = 240π + 441π
V_B = 681π
Now, we can approximate the volume of water in Container B to the nearest tenth of a cubic foot by calculating the value of 681π:
V_B ≈ 681π
V_B ≈ 681(3.14)
V_B ≈ 2141.34 cubic feet
Therefore, the volume of water in Container B, to the nearest tenth of a cubic foot, is approximately 2141.3 cubic feet.