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

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Intern
Joined: 13 Feb 2012
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If cylinder A has three times the height and one-third  [#permalink]

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18 Feb 2012, 10:59
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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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Joined: 02 Sep 2009
Posts: 64240
Re: If cylinder A has three times the height and one-third  [#permalink]

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18 Feb 2012, 11:10
1
tom09b 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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

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Re: If cylinder A has three times the height and one-third  [#permalink]

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03 Mar 2017, 22:51
Bunuel wrote:
tom09b 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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

Hi Bunuel,

The question states that the height of cylinder A is 3 times the height of cylinder B and the diameter if A is $$\frac{1}{3}$$ of cylinder B.
In the equation you've setup, I see that you've taken the radius of B as 3r and squared it. Is this a typo or am I misunderstanding the question.

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Joined: 02 Sep 2009
Posts: 64240
Re: If cylinder A has three times the height and one-third  [#permalink]

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04 Mar 2017, 01:12
Shruti0805 wrote:
Bunuel wrote:
tom09b 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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

Hi Bunuel,

The question states that the height of cylinder A is 3 times the height of cylinder B and the diameter if A is $$\frac{1}{3}$$ of cylinder B.
In the equation you've setup, I see that you've taken the radius of B as 3r and squared it. Is this a typo or am I misunderstanding the question.

Cylinder A has three times the height of cylinder B, so if the height of A is h then the height of B is h/3;
Cylinder A has one-third the diameter of cylinder B, so if the diameter of A is d, then the diameter of B is 3d. The same ratio will be for the radius too: if the radius of A is r, then the radius of B is 3r.

As for the squaring: it's because the formula for the volume of a cylinder is $$\pi{r}^2*h$$.

Hope it helps.
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Re: If cylinder A has three times the height and one-third  [#permalink]

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04 Mar 2017, 07:52
tom09b 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

For Cylinder B -

Height = x

$$Volume_B = π*(3x)^2*x => 9x^3π$$

For Cylinder A -

Height = 3x

$$Volume_A = π*(x)^2*3x => 3x^3π$$

$$\frac{Volume_A}{Volume_B} = \frac{3x^3π}{9x^3π}$$

So, $$\frac{Volume_A}{Volume_B} = 1:3$$

Thus, answer will be (C) 1 : 3
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Joined: 09 Jan 2017
Posts: 11
Re: If cylinder A has three times the height and one-third  [#permalink]

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04 Mar 2017, 08:54
Bunuel wrote:
tom09b 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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

Pay attention Bunuel
The question states that the cylinder A has 3 times the height and 1/3 the DIAMETER of cylinder B
It means that 1/3 DIAMETER= 2/3 RADIUS !!!!!
Math Expert
Joined: 02 Sep 2009
Posts: 64240
Re: If cylinder A has three times the height and one-third  [#permalink]

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05 Mar 2017, 02:41
marcuccio wrote:
Bunuel wrote:
tom09b 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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

Pay attention Bunuel
The question states that the cylinder A has 3 times the height and 1/3 the DIAMETER of cylinder B
It means that 1/3 DIAMETER= 2/3 RADIUS !!!!!

The question implies that cylinder A has three times the height than the height of B and cylinder A has one-third the diameter than the diameter of B.
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Re: If cylinder A has three times the height and one-third  [#permalink]

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05 Mar 2017, 02:44
Bunuel wrote:
marcuccio wrote:
Bunuel wrote:
[quote="tom09b"]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

$$Volume_A=\pi{r}^2*h$$;
$$Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h$$;

Ratio 1:3.

Pay attention Bunuel
The question states that the cylinder A has 3 times the height and 1/3 the DIAMETER of cylinder B
It means that 1/3 DIAMETER= 2/3 RADIUS !!!!!

The question implies that cylinder A has three times the height than the height of B and cylinder A has one-third the diameter than the diameter of B.[/quote]

What does it mean "one-third the diameter"???
It implies that 2/3 the radius.
Volume's formula use radius not diameter

Sent from my iPhone using GMAT Club Forum mobile app
Math Expert
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Posts: 64240
Re: If cylinder A has three times the height and one-third  [#permalink]

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05 Mar 2017, 02:52
marcuccio wrote:

What does it mean "one-third the diameter"???
It implies that 2/3 the radius.
Volume's formula use radius not diameter

Sent from my iPhone using GMAT Club Forum mobile app

Dear marcuccio,

Cylinder A has one-third the diameter of cylinder B, so if the diameter of A is 2, then the diameter of B is 6 --> the radius of A is 1, then the radius of B is 3.
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Re: If cylinder A has three times the height and one-third  [#permalink]

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17 Nov 2017, 11:03
To solve by plugging in:

Cylinder A:
H=3
D=2
V=1^2 x 3 x pi= 3pi

Cylinder B:
H=1
D=6
V=3^2 X 1 x pi= 9pi

Compare: 3pi:9pi reduced is 1:3
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If cylinder A has three times the height and one-third  [#permalink]

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11 Nov 2018, 23:06
tom09b 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

Let the radius and height of cylinder B be r and h respectively.
So, radius and height of cylinder A will be r/3 and 3h respectively.

Ratio of Volumes = $$({pi*{(\frac{r}{3})}^2*3h})/({pi*r^2*h})$$
=$$\frac{1}{3}$$
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Re: If cylinder A has three times the height and one-third  [#permalink]

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02 Jun 2019, 08:50
tom09b 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

let ha = 3
ra=1 ; da = 2
and hb=1
rb=3; db= 6
so ratio
pi * 1*3/ pi * 9*1 = 1/3
IMO C
Re: If cylinder A has three times the height and one-third   [#permalink] 02 Jun 2019, 08:50