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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Geometry

by BTGmoderatorRO » Fri Dec 29, 2017 9:16 am

A closed cylindrical tank contains 36Ï€ 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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Source: Beat The GMAT — Problem Solving | Fri Dec 29, 2017 9:16 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Fri Jan 05, 2018 4:58 am

Hello Roland2rule.

Let's take a look at your question.

We know that the cylindrical tank contains 36Ï€ cubic feet of water and is filled to half its capacity, it implies that its capacity is 72Ï€ 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 36Ï€, 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 [spoiler](B)=3[/spoiler].

I hope this explanation may help you.

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

Regards.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 02, 2019 5:57 pm

BTGmoderatorRO wrote:A closed cylindrical tank contains 36Ï€ 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

First we need to determine the radius of the circular base of the cylindrical tank. Recall that the volume of a cylinder is:

volume = Ï€(radius)^2(height)

Since half of the capacity of the tank is 36Ï€ and the height of the water is 4 feet, the full capacity of the tank is 72Ï€ and the full height of the tank is 8. Thus:

72Ï€ = Ï€r^2(8)

9 = r^2

3 = r

When the cylinder is on its side, the new height is represented by the diameter of the base. Since the cylinder is half full, the height of the water equals the radius of the base, which is 3.

Answer: B

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