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 10 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 Conainter 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?

Question

Tony Jensen

Mathematics

12 August, 22:22

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 10 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 Conainter 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?

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Answers (1)

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Gabriel Wilcox · Answer 1

Answer: The volume of empty space left is 854.1 cubic feet

Step-by-step explanation:

Before proceeding further, we need to put down the formula for calculating the volume of a cylinder = π*r^2*h

For container A, its diameter = 12feet. Since radius = diameter/2, then the radius of container A = 12/2 = 6feet. The height = 10feet, π will be taken as 3.14.

Now, we can plug these into the formula to calculate the volume of the cylinder A =

3.14 * 6 * 6 * 10 = 1,130.4 cubic feet.

So, if container A is filled with water, then the volume of the water that will be inside the container will be 1,130.4 cubic feet.

Again, we will also calculate the volume of the second cylindrical container (B). This time around, the height of container B is 17 feet and its diameter is 8 feet. This means that the radius of this particular container is = 8/2 = 4 feet. Since π is still 3.14, then the volume =

3.14 * 4 * 4 * 17 = 854.08 cubic feet.

So, if water is transferred from container A to container B until it is full. Then the quantity of water that will still be in container A after B is full =

1,130.4ft^3 - 854.08ft^3 = 276.32ft^3

This is the volume of water that will be left in container A. To calculate the volume of the empty space that is not currently occupied by water in container A, we will simply subtract the volume of water left in container A from the total or original volume of the container =

1,130.4 - 276.32 = 854.08 cubic feet.

Therefore the volume of the empty space left after water is transferred to container B until it is full is 854.1ft^3 (to the nearest tenth of a cubic foot)