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Two oil cans, X and Y, are right circular cylinders, and the height an

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Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

(A) $1
(B) $2
(C) $3
(D) $4
(E) $8

Originally posted by cucrose on 17 Feb 2007, 15:25.
Last edited by Bunuel on 15 Jun 2017, 01:17, edited 2 times in total.
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 17 Feb 2007, 16:56
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Volume of x(Vx) is r^2*PI*h (r-radius, h height)

Volume of y (Vy) is (2r)^2*PI*2h = 4*r^2*PI*2h=8r^2*PI*h = 8*Vx

If Vx is 2$
Vy/2=4*Vx=8$
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 17 Feb 2007, 21:28
cucrose wrote:
Oil cans x and y are right circular cylinders and the height and radius of y are each twice those of x. If the oil in can x filled to capacity sells for $2, how much does the oil in y sell for if y is only half filled?

A $1
B $2
C $3
D $4
E $8

Can someone please explain this one? thanks.


formula for vol of a cyl is PI*r^2*h

so Vy = 8*Vy

y when half filled will cost 4 times x so ans is E
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 05 Mar 2012, 23:28
can you help me,where are you getting 8 since volume of y is on 2r *Pi*2h,as stated on the question?

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Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 06 Mar 2012, 05:35
Andrew222 wrote:
can you help me,where are you getting 8 since volume of y is on 2r *Pi*2h,as stated on the question?

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Welcome to GMAT Club. Below is a complete step-by-step solution of the question.

Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

(A) $1
(B) $2
(C) $3
(D) $4
(E) $8

The volume of can X is \(\pi{r^2}h\), which when filled to capacity sells for $2;

The volume of can Y is \(\pi{(2r)^2}(2h)=8\pi{r^2}h\). Can Y is only half fill so volume of oil in it is \(4\pi{r^2}h\). Since \(\pi{r^2}h\) sells for $2 then \(4\pi{r^2}h\) sells for 4*$2=8$.

Answer: E.

Hope its clear.
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 16 Mar 2012, 01:24
Thank you i can now get you what you were doing to get the answer

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Re: Two oil cans,X and Y,are right circular cylinders,and the he  [#permalink]

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New post 21 Jan 2013, 02:51
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Let us suppose the radius and height of can X are r and h respectively. So the radius and height of can Y will be 2r and 2h respectively.
Volume of X = 3.14 * r^2 * h
Volume of Y = 3.14 * (2r)^2 * 2h = 8 * 3.14 * r^2 * h = 8 times of X's volume.
Since X is sold for $2, and Y is filled to only half of its capacity, Y will be sold for 4 * $2 ( half of Y's volume = 8/2 * X's volume ) = $8.
Hence E is the answer.
Please provide Kudos if you like my explanation.
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Re: Two oil cans,X and Y,are right circular cylinders,and the he  [#permalink]

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New post 21 Jan 2013, 03:20
no doubt at abhii6 you..you deserve a kudos.. +1 for nice reply..hey i have never done a kudos before but i guess thats how it is done..if not then please tell me i will readily redo it

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Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 15 Jun 2017, 08:14
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cucrose wrote:
Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

(A) $1
(B) $2
(C) $3
(D) $4
(E) $8

Choose values. Volume of a right circular cylinder is \(\pi{r^2}h\).

Let radius of X = 1, and height of X = 2.

Radius and height of Y are each twice that of X. Radius of Y = 2, height = 4.

So volume of X is \((\pi)(1^2)(2)\) = \(2\pi\)

Volume of Y = \((\pi)(2^2)(4)\) = \(16\pi\).
But Y is only half full, so the volume of oil that Y contains is \(8\pi\)

Let Z = the sell price of the oil in can Y.

\(\frac{Price.Of.X.Oil}{Volume.X}=\frac{Z}{Volume.Y}\)

\(\frac{$2}{(2\pi)} = \frac{Z}{(8\pi)}\)

Z = $8, Answer E
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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New post 17 Jun 2017, 05:27
cucrose wrote:
Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

(A) $1
(B) $2
(C) $3
(D) $4
(E) $8


We can let the radius of X = r and the height of X = h; thus, the radius of Y = 2r and the height of Y = 2h.

Thus, the volume of cylinder X is πr^2h and the volume of cylinder Y is:

π[(2r)^2](2h) = 8πr^2h

Since cylinder X is filled to its capacity, the volume of oil in X is πr^2h. However, since cylinder Y is only filled to half of its capacity, the volume of oil in Y is 4πr^2h. Since the oil in X sells for $2, at the same rate, the oil in Y should sell for 4 times as much (since it has 4 times as much oil), or $8.

Answer: E
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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Re: Two oil cans, X and Y, are right circular cylinders, and the height an   [#permalink] 05 Mar 2019, 23:35
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