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# 2. (KP) Can A and can В are both right circular cylinders. T

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2. (KP) Can A and can В are both right circular cylinders. T [#permalink]  17 Mar 2011, 14:46
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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
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]  17 Mar 2011, 15:09
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

Ans E
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]  19 Mar 2011, 01:57
B -> pi * r^2*h

A -> pi * 4r^2 * h/2 = 2 * pi * r^2 * h

So, Vol of 1/2 of can B = vol of 1/4 can A

So can A will take 4 * 4 = \$16 for gasoline.
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Manager
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Kudos [?]: 12 [0], given: 8

Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]  19 Mar 2011, 02:52
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\$
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink]  19 Mar 2011, 03:05
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.
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Re: 2. (KP) Can A and can В are both right circular cylinders. T   [#permalink] 19 Mar 2011, 03:05
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