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

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

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

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New post 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.

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

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New post 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.

Answer: C.


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.

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

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New post 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.

Answer: C.


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.

Thanks in advance.


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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New post 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
Radius = 3x

\(Volume_B = π*(3x)^2*x => 9x^3π\)

For Cylinder A -

Height = 3x
Radius = x

\(Volume_A = π*(x)^2*3x => 3x^3π\)

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

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

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

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New post 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.

Answer: C.


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 !!!!!
DIAMETER= 2*RADIUS
:!: :!: :!: :!: :!: :!: :!: :!: :!:
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Re: If cylinder A has three times the height and one-third  [#permalink]

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New post 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.

Answer: C.


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 !!!!!
DIAMETER= 2*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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New post 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.

Answer: C.


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 !!!!!
DIAMETER= 2*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


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

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New post 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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Collection of Questions:
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Re: If cylinder A has three times the height and one-third  [#permalink]

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New post 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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New post 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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If cylinder A has three times the height and one-third &nbs [#permalink] 11 Nov 2018, 23:06
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