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 16 feet. Container B has a diameter of 18 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 the empty space inside 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.
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height.
For Container A:
Radius = 22 feet / 2 = 11 feet
Height = 16 feet
V(A) = π(11)^2(16) ≈ 6197.92 cubic feet
For Container B:
Radius = 18 feet / 2 = 9 feet
Height = 17 feet
V(B) = π(9)^2(17) ≈ 4572.41 cubic feet
Now, we need to find how much water will be transferred from Container A to Container B:
V_transferred = V(A) - V(B) ≈ 1625.51 cubic feet
After transferring the water, the volume of the empty space in Container A will be:
V_empty_space(A) = V(A) - V_transferred ≈ 4572.41 cubic feet
Therefore, the volume of the empty space inside Container A, to the nearest tenth of a cubic foot, is approximately 4572.4 cubic feet.
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 16 feet. Container B has a diameter of 18 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 the empty space inside Container A, to the nearest tenth of a cubic foot?
First, let's calculate the volume of water in Container A and Container B.
For Container A:
Radius of container A = diameter / 2 = 22 feet / 2 = 11 feet
Height of container A = 16 feet
Volume of water in Container A = π(11)^2(16) = 6168.48 cubic feet
For Container B:
Radius of container B = diameter / 2 = 18 feet / 2 = 9 feet
Height of container B = 17 feet
Volume of water in Container B = π(9)^2(17) = 4592.63 cubic feet
The amount of water transferred from Container A to Container B is:
Volume transferred = Volume of water in Container A - Volume of water in Container B
Volume transferred = 6168.48 - 4592.63 = 1575.85 cubic feet
After the pumping is complete, the volume of the empty space inside Container A is the volume of water remaining in Container A:
Volume of empty space inside Container A = Volume of water in Container A - Volume transferred
Volume of empty space inside Container A = 6168.48 - 1575.85 = 4592.63 cubic feet
Therefore, the volume of the empty space inside Container A, to the nearest tenth of a cubic foot, is approximately 4592.6 cubic feet.