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OG Closed cylindrical tank Q

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Closed cylindrical tank Q

Post Tue Jul 25, 2017 8:09 pm
A closed cylindrical tank contains 36pi 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

B

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Post Mon Aug 14, 2017 1:17 pm
AbeNeedsAnswers wrote:
A closed cylindrical tank contains 36pi 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

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

volume = π(radius)^2(height)

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

72π = πr^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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Post Tue Jul 25, 2017 11:29 pm
AbeNeedsAnswers wrote:
A closed cylindrical tank contains 36pi 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

B
We know that the with half the volume, the height of the water level is 4 feet, thus, the height of the cylinder = 2*4 = 8 feet.

Since the volume of water = 36π, which is half of the volume of the cylinder, the volume of the cylinder = 2*36π = 72π cubic feet

=> volume of the cylinder = πr^2h = 72π

8πr^2 = 72π; since h = 8

Thus, r = 3 feet

When the tank is placed on its side on level ground, the height of the surface of the water above the ground would be equal to the radius of the cylinder = 3 feet

The correct answer: B

Hope this helps!

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