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Rate Filling Tank = Radius

by bml1105 » Mon May 19, 2014 9:38 am
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: B
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Rate Filling Tank = Radius

by Brent@GMATPrepNow » Mon May 19, 2014 9:50 am
bml1105 wrote: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
Let's examine what occurs in a 1-hour period
The volume of water increases by 22 cubic meters.
The height of the water increases by 0.7 meters.

So, we need to find the radius of a 0.7 meter high cylinder that has a volume of 22 cubic meters.

Volume = (pi)r²h
22 = (pi)r²(0.7)

IMPORTANT: notice that (pi)(0.7) = approximately 2.2

So, we get: 22 = (2.2)r²
Divide both sides by 2.2: 10 = r²
Solve: r = √10 (approximately)

Answer: B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Mar 02, 2018 3:40 pm, edited 1 time in total.
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by [email protected] » Mon May 19, 2014 10:37 am
Hi bml1105,

This question can also be solved by TESTing THE ANSWERS.

Volume of a cylinder is...

V = (pi)(R^2)H

With a given height of .7 meters, we can TEST the answers to find the one that gives us a Volume of 22.

While I would normally start with B or D, I'm going to start with C (since it's the smallest of the "nice" answers and it's right in the "middle" of the options)

If R = 4, we'd have....

(pi)(4^2)(.7) = 16pi(.7) = approximately 35

This result is TOO BIG (it's supposed to be 22). This means we can eliminate C and anything bigger than C (D and E).

Let's test B next. If R = √10.....

(pi)(10)(.7) = 7pi = approximately 22. This is a MATCH for what we were told.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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