Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 feet and a height of 8 feet. Container B has a diameter of 8 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 water remaining in Container A, to the nearest tenth of a cubic foot?
First, we need to calculate the volume of water in Container A and Container B.
Volume of a cylinder is calculated using the formula:
V = πr^2h
Where:
V = volume
r = radius of the cylinder
h = height of the cylinder
For Container A:
Radius = Diameter / 2 = 14 / 2 = 7 feet
Height = 8 feet
V(A) = π * 7^2 * 8 = 1,232.4 cubic feet
For Container B:
Radius = Diameter / 2 = 8 / 2 = 4 feet
Height = 17 feet
V(B) = π * 4^2 * 17 = 863.94 cubic feet
Now, we need to find the volume of water that was transferred from Container A to Container B. This is the difference between the initial volume of water in Container A and the final volume of water in Container B.
Volume of water transferred = V(A) - V(B)
Volume of water transferred = 1,232.4 - 863.94 = 368.46 cubic feet
Therefore, the volume of water remaining in Container A after the pumping is complete is approximately 368.5 cubic feet.
incorrect
I apologize for the error in my previous response. Let me correct the calculation:
The volume of water in Container A is calculated using the formula for the volume of a cylinder:
V(A) = πr^2h
For Container A:
Radius = Diameter / 2 = 14 / 2 = 7 feet
Height = 8 feet
V(A) = π * 7^2 * 8 = 1,232 cubic feet
After pumping the water from Container A to Container B, the volume of water in Container B will be equal to the volume of Container B, which is:
V(B) = π * (8/2)^2 * 17 = 452π ≈ 1419.88 cubic feet
Therefore, the volume of water transferred from Container A to B is:
Volume transferred = V(A) - V(B) = 1,232 - 1419.88 ≈ -187.88
As the calculated volume transferred is negative, it means there was not enough water in Container A to fill Container B completely. So, all the water from Container A would have been transferred to Container B.
Therefore, the correct answer is that there is no water remaining in Container A after pumping all the water to Container B.