Two containers designed to hold water are side by side in a cylinder shape. Container A has a diameter of 18 feet and a height of 16 feet. Container B has a diameter of 12 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until it is 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 volumes of both containers.
The volume of container A can be calculated using the formula for the volume of a cylinder:
V = πr^2h
Where r is the radius of the container (which is half the diameter), and h is the height.
For container A:
r = 18/2 = 9 feet
h = 16 feet
V_A = π(9^2)(16) = 4069.8 cubic feet
The volume of container B can be calculated in the same way:
r = 12/2 = 6 feet
h = 20 feet
V_B = π(6^2)(20) = 2261.9 cubic feet
After pumping the water from container A to container B, the volume of water in container B will be 4069.8 cubic feet + 2261.9 cubic feet = 6331.7 cubic feet.
The volume of the empty space inside container A can be calculated by subtracting the volume of water in container B from the volume of container A:
Empty space volume = V_A - V_B = 4069.8 cubic feet - 2261.9 cubic feet = 1807.9 cubic feet
So, the volume of the empty space inside container A is 1807.9 cubic feet to the nearest tenth of a cubic foot.