When a cylindrical tank is filled with water

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Dec 12, 2017 4:35 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. âˆš10/2
B. âˆš10
C. 4
D. 5
E. 10

Can some experts give a simple solution in this problem?

OA B

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Source: Beat The GMAT — Problem Solving | Tue Dec 12, 2017 4:35 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Dec 12, 2017 5:03 am

lheiannie07 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. âˆš10/2
B. âˆš10
C. 4
D. 5
E. 10

Ï€ â‰ˆ 22/7.

After 1 hour, the volume in the tank = 22 cubic meters, with a height of 0.7 meters.
Since V = Ï€rÂ²h, we get:
22 = Ï€(rÂ²)(0.7)
22 = (22/7)(rÂ²)(7/10)
1 = rÂ²/10
10 = rÂ²
âˆš10 = r.

The correct answer is B.

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Tue Dec 12, 2017 5:18 am

lheiannie07 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. âˆš10/2
B. âˆš10
C. 4
D. 5
E. 10

Can some experts give a simple solution in this problem?

OA B

if r is the radius of the cylinder then it would get filled @ (Ï€r^2 )*0.7
Therefore (Ï€r^2 )*0.7=22
Put the value of Ï€ as 22/7 and you get
[(22/7)r^2 ]*0.7= 22
Solving this you get r^2=7/0.7=10
Or r=âˆš10
Hence B is the correct option

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