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# If cylinder A has three times the height and one -third the diameter

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Math Expert
Joined: 02 Sep 2009
Posts: 56268
If cylinder A has three times the height and one -third the diameter  [#permalink]

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22 Feb 2018, 20:36
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Difficulty:

55% (hard)

Question Stats:

67% (01:57) correct 33% (01:42) wrong based on 53 sessions

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If cylinder A has three times the height and one -third the diameter of cylinder B, what is the ratio of the volume of A to the volume of B ?

(A) 3:1

(B) 1:1

(C) 1:3

(D) 1:9

(E) 1:27

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Intern
Joined: 09 Apr 2017
Posts: 4
Re: If cylinder A has three times the height and one -third the diameter  [#permalink]

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22 Feb 2018, 22:35
volume of a Cyclinder = 1/3*pi*r square*h , the variables are the radius and height . if diameter is reduced by 1/3 , then radius also reduced by 1/3 , height is increased 3 times.

vol a / vol b will be
->r square*h / 1/9 rsquare * 3h
-> 1/ 1/3
-> 3/1

Retired Moderator
Joined: 07 Jan 2016
Posts: 1090
Location: India
GMAT 1: 710 Q49 V36
Re: If cylinder A has three times the height and one -third the diameter  [#permalink]

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23 Feb 2018, 00:48
Bunuel wrote:
If cylinder A has three times the height and one -third the diameter of cylinder B, what is the ratio of the volume of A to the volume of B ?

(A) 3:1

(B) 1:1

(C) 1:3

(D) 1:9

(E) 1:27

v= 1/3 pi r^h

v1/v2 = r1^2 h 1 / r2^2 h2

h1 = 3h2

d1 = 1/3d2

2r1 = 1/3 2r2

r1 = r2/3

3r1 = r2

v1 = r1 ^2 h 1 = r2/9 x 3 h2 = r2^2h2/3

v2 = r2^2 h2

v1/v2 = 1/3
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9441
Location: Pune, India
Re: If cylinder A has three times the height and one -third the diameter  [#permalink]

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23 Feb 2018, 01:02
Bunuel wrote:
If cylinder A has three times the height and one -third the diameter of cylinder B, what is the ratio of the volume of A to the volume of B ?

(A) 3:1

(B) 1:1

(C) 1:3

(D) 1:9

(E) 1:27

Vol of cylinder $$= \pi*r^2*h$$

One third the diameter means one third the radius too.

$$\frac{Vol of A}{Vol of B} = \frac{\pi * (r/3)^2 * 3h}{\pi * r^2 * h} = \frac{1}{3}$$

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Karishma
Veritas Prep GMAT Instructor

Re: If cylinder A has three times the height and one -third the diameter   [#permalink] 23 Feb 2018, 01:02
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