OG Closed cylindrical tank Q

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 394
Joined: 02 Jul 2017
Thanked: 1 times
Followed by:4 members

OG Closed cylindrical tank Q

by AbeNeedsAnswers » Tue Jul 25, 2017 8:09 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: 22 Aug 2016
Location: Grand Central / New York
Thanked: 470 times
Followed by:32 members

by [email protected] » 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 = 36Ï€, which is half of the volume of the cylinder, the volume of the cylinder = 2*36Ï€ = 72Ï€ cubic feet

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

8Ï€r^2 = 72Ï€; 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!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 6229
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members

by [email protected] » 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 36Ï€ and the height of the water is 4 feet, the full capacity of the tank is 72Ï€ 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:508 members
GMAT Score:800

Re: OG Closed cylindrical tank Q

by [email protected] » Sun Apr 18, 2021 3:21 pm
Hi All,

We’re told that a cylindrical tank (re: a cylinder/tube) contains 36pi cubic feet of water and is filled to HALF of its capacity; when placed upright, the water reaches 4 feet high. We’re asked how high the water reaches when the tank is placed on its side.

One of the ‘keys’ to solving this question quickly is to realize that since the tank is half-full, regardless of which side the tank is laying on, the water will reach HALF of the height.

Volume of a cylinder is (pi)(Radius^2)(Height), so we can use that formula – along with what we know about the water – to figure out the radius of the tank…

V = (pi)(R^2)(H) =
36pi = (pi)(R^2)(4)
36 = (R^2)(4)
9 = R^2
R = 3

Thus, the radius of the tank is 3 feet and its diameter is 6 feet. When the cylinder is lying on its side, the water will go to the half-way point of the cylinder. Since the diameter is 6 feet, the half-way point would be the radius: 3 feet.

Final Answer: B

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