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 19 feet. Container B has a diameter of 28 feet and a height of 18 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 the empty portion of Container B, to the nearest tenth of a cubic foot?
First, we need to calculate the volume of water in Container A using the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the cylinder and h is the height.
For Container A:
Radius = diameter/2 = 22/2 = 11 feet
Height = 19 feet
Volume of water in Container A:
V = π(11)^2(19) ≈ 7526.53 cubic feet
Next, we need to calculate the total volume of Container B, including the water pumped from Container A.
For Container B:
Radius = diameter/2 = 28/2 = 14 feet
Height = 18 feet
Volume of Container B:
V = π(14)^2(18) ≈ 11304.79 cubic feet
The volume of water pumped from Container A to Container B is 7526.53 cubic feet, so the volume of the empty portion of Container B is:
11304.79 - 7526.53 = 3778.26 cubic feet
Therefore, the volume of the empty portion of Container B is approximately 3778.3 cubic feet to the nearest tenth.
Wrong
Let's try solving this problem again:
The volume of the cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
For Container A:
Radius = diameter/2 = 22/2 = 11 feet
Height = 19 feet
Volume of water in Container A:
V = π(11)^2(19) = 23231.03 cubic feet
Now, the water is pumped from Container A to Container B.
For Container B:
Radius = diameter/2 = 28/2 = 14 feet
Height = 18 feet
The total volume of Container B is:
V = π(14)^2(18) = 11447.23 cubic feet
After pumping the water from Container A to Container B, the volume of water in Container B is 23231.03 cubic feet.
So, the volume of the empty portion of Container B is:
11447.23 - 23231.03 = -11783.8 cubic feet
This result is negative because the water from Container A completely filled Container B and overflowed. Therefore, the correct answer is that the volume of the empty portion of Container B is 0 cubic feet.
Still wrong
I apologize for the error. Let's correct it:
The volume of water in Container A is correct at 23231.03 cubic feet.
When the water is transferred to Container B, the total volume of water in Container B is now 23231.03 cubic feet as it is filled to the same level as Container A.
Now, we need to calculate the total volume of Container B:
For Container B:
Radius = 14 feet
Height = 18 feet
Volume of Container B:
V = π(14)^2(18) ≈ 11304.79 cubic feet
To find the volume of the empty portion of Container B, we subtract the volume of water in Container B (23231.03 cubic feet) from the total volume of Container B:
11304.79 - 23231.03 ≈ -11926.24 cubic feet
Since the answer is negative, it means that Container B is completely filled with water, and there is no empty portion left.
Therefore, the volume of the empty portion of Container B, after transferring the water from Container A, is 0 cubic feet.