Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 17 feet. Container B has a diameter of 22 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.

To the nearest tenth, what is the percent of Container A that is empty after the pumping is complete?

Answer 1

The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

The radius of container A is 13 feet (since the diameter is 26 feet), and the height is 17 feet. Therefore, the volume of container A is:

V_A = π(13)^2(17) ≈ 9563.3 cubic feet

The radius of container B is 11 feet (since the diameter is 22 feet), and the height is 20 feet. Therefore, the volume of container B is:

V_B = π(11)^2(20) ≈ 7622.2 cubic feet

When the water is pumped from container A to container B, the volume of water moved is equal to the difference in the volumes of the two containers:

V_water = V_A - V_B ≈ 1941.1 cubic feet

The percent of container A that is empty after the pumping is complete is equal to the volume of water moved, divided by the volume of container A, multiplied by 100:

percent empty = (V_water / V_A) x 100

percent empty ≈ 20.3%

Therefore, to the nearest tenth, the percent of container A that is empty after the pumping is complete is 20.3%.

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