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Intern  Joined: 08 Jan 2007
Posts: 34
Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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Question Stats: 74% (01:40) correct 26% (01:38) wrong based on 353 sessions

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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.
Edited the question
Intern  Joined: 04 Apr 2006
Posts: 24
Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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1
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$Vy/2=4*Vx=8$
Senior Manager  Joined: 12 Mar 2006
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Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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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
Intern  Joined: 04 Mar 2012
Posts: 2
Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
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Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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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?

Posted from my mobile device

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*$2=8$.

Hope its clear.
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Intern  Joined: 04 Mar 2012
Posts: 2
Re: Two oil cans, X and Y, are right circular cylinders, and the height an  [#permalink]

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Thank you i can now get you what you were doing to get the answer

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Manager  Joined: 12 Mar 2012
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GMAT 1: 710 Q49 V36 GPA: 3.2
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Re: Two oil cans,X and Y,are right circular cylinders,and the he  [#permalink]

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1
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. Manager  Joined: 04 Jan 2013 Posts: 68 Re: Two oil cans,X and Y,are right circular cylinders,and the he [#permalink] Show Tags 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 Posted from my mobile device Senior SC Moderator V Joined: 22 May 2016 Posts: 3581 Two oil cans, X and Y, are right circular cylinders, and the height an [#permalink] Show Tags 1 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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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.

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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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