Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 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?
To find the volume of the empty space inside Container A, we first need to calculate the volume of water that was pumped from Container A to Container B.
The formula to calculate the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
For Container A:
r = 12 ft / 2 = 6 ft
h = 9 ft
So, the volume of water in Container A is:
V_A = π(6)^2(9) = 324π cubic feet
For Container B:
r = 8 ft / 2 = 4 ft
h = 20 ft
So, the volume of water in Container B is:
V_B = π(4)^2(20) = 320π cubic feet
The volume of water pumped from Container A to Container B is:
V_pumped = V_A - V_B
V_pumped = 324π - 320π
V_pumped = 4π cubic feet
Now, the volume of empty space inside Container A is just the volume of the cylinder minus the volume of water that was pumped:
V_empty_A = V_A - V_pumped
V_empty_A = 324π - 4π
V_empty_A = 320π cubic feet
To find the value in terms of pi, we can use the approximation π ≈ 3.14:
V_empty_A ≈ 320(3.14)
V_empty_A ≈ 1004.8 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 1004.8 cubic feet.
Try one more time
Apologies for the mistake. Let's try this one more time.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
For Container A:
Radius (r) = 12 ft / 2 = 6 ft
Height (h) = 9 ft
Volume of Container A = π(6)^2(9) = 324π cubic feet
For Container B:
Radius (r) = 8 ft / 2 = 4 ft
Height (h) = 20 ft
Volume of Container B = π(4)^2(20) = 320π cubic feet
Since all the water in Container A is transferred to Container B, the volume of empty space in Container A is the difference between the volume of Container A and the volume of water transferred.
Volume of empty space inside Container A = 324π - 320π = 4π cubic feet
Using the approximation π ≈ 3.14, we have:
Volume of empty space inside Container A ≈ 4(3.14) = 12.56 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 12.56 cubic feet.
Try again
Let's try this one more time:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
For Container A:
Radius (r) = 12 ft / 2 = 6 ft
Height (h) = 9 ft
Volume of Container A = π(6)^2(9) = 324π cubic feet
For Container B:
Radius (r) = 8 ft / 2 = 4 ft
Height (h) = 20 ft
Volume of Container B = π(4)^2(20) = 320π cubic feet
Since all the water in Container A is transferred to Container B, the volume of empty space in Container A is the volume of Container A minus the volume of water that was transferred.
Volume of empty space inside Container A = 324π - 320π = 4π cubic feet
Using the approximation π ≈ 3.14, we have:
Volume of empty space inside Container A ≈ 4(3.14) = 12.56 cubic feet
Therefore, the volume of the empty space inside Container A is approximately 12.56 cubic feet.