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

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

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