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Can A and can В are both right circular cylinders. The radiu [#permalink]

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17 Mar 2011, 13:46

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Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?

Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]

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17 Mar 2011, 14:09

banksy wrote:

2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline? (A) $1 (B) $2 (C) $4 (D) $8 (E) $16

Let x be the radius of b and 2h be the height of B. Therefore, radius of A = 2x and height = h

Vol of b = 3.14*x^2*2h Vol of a = 3.14*4x^2*h

cost to fill half of B = $4 --> cost to fill full B = $8 --> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16

Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]

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19 Mar 2011, 01:52

banksy wrote:

2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline? (A) $1 (B) $2 (C) $4 (D) $8 (E) $16

Let radius of B be r and A be 2r vol of B=πr^2h vol of a=4πr^2h (radius= (2r)) == twice the volume of B

To fill 1/2 of B it cost 4$ to fill B it cost 8 $ to fill 2b ie (a) it cost 16$

Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]

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19 Mar 2011, 02:05

banksy wrote:

2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline? (A) $1 (B) $2 (C) $4 (D) $8 (E) $16

Volume of right circular cylinder = 2πr^2h Let Radius of Can A= 4 Height of can A = 2 Volume of Can A = 2*π*r^2*h = 2*π*4^2*2 = 64π

Radius of can B = 2 Height of can B = 4 Volume of Can B= 2*π*r^2*h = 2*π*2^2*4 = 32π

1/2 of B= 32π/2=16π

thus cost required to fill can A = (4/16π)*64π= $16 Ans E.
_________________

Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]

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22 Sep 2013, 19:34

sorry guys the answer is $ 8. lets consider the radius of can A to be 2x. radius of can B to be x. let the height of can A be y. Let the height of can B be 2y. Volume of a can A (pie 4x^2y) Volume of can B (pie 2 x^2 y). Since volume of can B is exactly half of can A. It costs $8 to fill can A completely.

sorry guys the answer is $ 8. lets consider the radius of can A to be 2x. radius of can B to be x. let the height of can A be y. Let the height of can B be 2y. Volume of a can A (pie 4x^2y) Volume of can B (pie 2 x^2 y). Since volume of can B is exactly half of can A. It costs $8 to fill can A completely.

Notice that we a re told that it costs $4.00 to fill half of can B. so the correct answer is E, not D.

Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?

(A) $1 (B) $2 (C) $4 (D) $8 (E) $16

Volume of B = \(\pi{r^2}h\) Volume of A = \(\pi{(2r)^2}(\frac{h}{2})=2\pi{r^2}h\).

Thus the volume of can A is twice the volume of cam B.

If it costs $4.00 to fill half of can B, then it costs 4*$4=$16 to completely fill can A.

Re: Can A and can В are both right circular cylinders. The radiu [#permalink]

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27 Jan 2016, 23:07

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Re: Can A and can В are both right circular cylinders. The radiu [#permalink]

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02 Feb 2016, 14:48

Hey guys,

one question. I first tried to pick some smart numbers. Apparently they weren't smart enough as I did not get the volume of cylinder A to be twice the volume of cylinder B. I picked 4 and 2 for radii and 3 and 6 for heights. Of course, if we pick 4 and 2 for radii and 2 and 4 for heights, we are fine. So my question then is, if I for whatever reason at the actual test decide to go with smart numbers strategy for such a problem, how can I avoid this mistake? What am I missing here?

one question. I first tried to pick some smart numbers. Apparently they weren't smart enough as I did not get the volume of cylinder A to be twice the volume of cylinder B. I picked 4 and 2 for radii and 3 and 6 for heights. Of course, if we pick 4 and 2 for radii and 2 and 4 for heights, we are fine. So my question then is, if I for whatever reason at the actual test decide to go with smart numbers strategy for such a problem, how can I avoid this mistake? What am I missing here?

Appreciate your help as always!

Best, Jay

Nothing! These numbers are fine too. You probably messed up the calculations somewhere.

Volume of a right circular cylinder \(= \pi*r^2*h\)

Volume of can A \(= \pi * 4^2* 3 = 48* \pi\) Volume of can B \(= \pi * 2^2 * 6 = 24* \pi\)

Volume of can A is twice the volume of can B.

OF course, you can stick with radii as 2r and r and heights as h and 2h since you just need the comparative volumes of the two cans.
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