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radius of a cylinder

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by Fdelpesce » Sat Jan 12, 2013 5:18 pm
Can someone help explain this problem and how to get the correct answer please. It is from the Manhattan gmat site and i don't fully understand their explanation.

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10


Correct answer is B.

Thank you!
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by GMATGuruNY » Sat Jan 12, 2013 6:18 pm
Fdelpesce wrote:Can someone help explain this problem and how to get the correct answer please. It is from the Manhattan gmat site and i don't fully understand their explanation.

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10
In the course of an hour:
The VOLUME increases by 22 cubic meters.
The HEIGHT increases by .7 meters.
Thus:
V = 22 when h = .7.

Since V = �r²h and � ≈ 3, we get:
22 = �r²(.7)
22 = (3)r²(.7)
r² = 22/2.1
r² ≈ 10
r ≈ √10.

The correct answer is B.
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by Fdelpesce » Sat Jan 12, 2013 6:57 pm
How do you transition from 22 = (3)r²(.7) to r² = 22/2.1? Don't you have to divide by r² since they are all multiplied together? Which would give you 22/r² on the left side. I get confused between subtracting and dividing to get the figure on the opposite side of the equation because I thought when there is multiplication involved you divide and when its addition/subtraction you either add or subtract?

Very much appreciated GMATGuru!
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by GMATGuruNY » Sat Jan 12, 2013 7:15 pm
Fdelpesce wrote:How do you transition from 22 = (3)r²(.7) to r² = 22/2.1? Don't you have to divide by r² since they are all multiplied together? Which would give you 22/r² on the left side. I get confused between subtracting and dividing to get the figure on the opposite side of the equation because I thought when there is multiplication involved you divide and when its addition/subtraction you either add or subtract?

Very much appreciated GMATGuru!
Step by step:

22 = (3)r²(.7)

22 = (2.1)r² Multiply (3)(.7) = 2.1.

22/(2.1) = r² Divide each side by 2.1.

220/21 = r² To clear the decimal, multiply 22/(2.1) * 10/10 = 220/21.

10 ≈ r² Approximate that 220/21 ≈ 10.

√10 = √r² Take the square root of both sides.

√10 = r. Simplify the righthand side.
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