Question

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 19 feet. Container B has a diameter of 16 feet and a height of 12 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 water in Container B, to the nearest tenth of a cubic foot?

Answer 1

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

For Container A, the radius is half the diameter, so r = 6 feet. The volume of water in Container A is V_A = π(6^2)(19) ≈ 2154.4 cubic feet.

After pumping all the water from Container A into Container B, the height of the water in Container B will be the same as the height of Container A, which is 19 feet. The radius of Container B is half the diameter, so r = 8 feet. The volume of water in Container B is therefore V_B = π(8^2)(19) ≈ 3831.0 cubic feet.

Subtracting the volume of water that was originally in Container A, we get:

V_B - V_A ≈ 3831.0 - 2154.4 ≈ 1676.6 cubic feet

Therefore, the volume of water in Container B after pumping is approximately 1676.6 cubic feet to the nearest tenth.