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Geometry

This topic has 1 expert reply and 0 member replies

Geometry

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A closed cylindrical tank contains 36π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

OA is B

What is the right formula to solve this question? An Expert analysis is required here, please. Thanks

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GMAT/MBA Expert

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Hello Roland2rule.

Let's take a look at your question.

We know that the cylindrical tank contains 36π cubic feet of water and is filled to half its capacity, it implies that its capacity is 72π cubic feet. On the other hand, the volume of the cylindrical tank is $$V=\pi r^2h$$ where r is the radius of the base and h the height of the tank. So, we can set the equation $$72\pi=\pi r^2h\ \ \ \Leftrightarrow\ \ \ r^2h=72.$$ Now let's read the following "when the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet", that is to say, we have a cylindrical tank with h=4 feet and volume equals to 36π, then $$\pi r^2h=36\pi\ \Leftrightarrow\ \ r^2\cdot4=36\ \Leftrightarrow\ r^2\ =\ 9\ \Leftrightarrow\ \ r=3\ feet.$$ Now, we are asked: "When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?", but we have to remember that the tank is filled to half its capacity, so when it is placed on its side, the height of the water is half of the height of the diameter of the circle, that is to say, the radius. It implies that the height of the water is r=3.

This is why the correct answer is (B)=3.

I hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.

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