Question bank / Area and volume

Math · Geometry and TrigonometryHard

A cylindrical tank with a radius of 33 feet and a height of 88 feet contains water to a depth of 55 feet. All of the water is poured into an empty cylindrical tank with a radius of 55 feet. What is the depth, in feet, of the water in the second tank?

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Answer: 1.8

The volume of water is π(3)2(5)=45π\pi(3)^2(5) = 45\pi cubic feet; the tank's full height of 88 feet doesn't matter. In the second tank, π(5)2h=45π\pi(5)^2 h = 45\pi, so 25h=4525h = 45 and h=1.8h = 1.8 feet.

Using the full height of 88 feet gives 72π72\pi cubic feet and a depth of 2.882.88, but only the water, not the whole tank, is poured.

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