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# A cylindrical tank, with radius and height both of 10 feet,

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VP
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A cylindrical tank, with radius and height both of 10 feet, [#permalink]

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14 Nov 2005, 13:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A cylindrical tank, with radius and height both of 10 feet, is to be redesigned as a cone, capable of holding twice the volume of the cylindrical tank. There are two proposed scenarios for the new cone: in scenario
(1) the radius will remain the same as that of the original cylindrical tank, in scenario
(2) the height will remain the same as that of the original cylindrical tank.

What is the approximate difference in feet between the new height of the cone in scenario (1) and the new radius of the cone in scenario (2)?
(The formula for the volume of a cone is V = 1/3 pi r^2 h).

(A) 13
(B) 25
(C) 30
(D) 35
(E) 40
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VP
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14 Nov 2005, 13:52
D)...old volume is 1000pi and new volume is 2000pi

I. 1/3pi*100*h=2000pi => h=60
II. 1/3pi*10*r^2=2000pi => r~24

h-r~35

hm ? seems to be too easy...
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Director
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14 Nov 2005, 14:34
D

2* pi*r^2*10=1/3*pi*r^2*h1 ==> h1=60

2) height same
2*pi*10^2*10=1/3*pi*r2^2*10
r2^2=3*10^2
r2 = 10*sqrt(3)=10*1.732*1.44=24.8~25

Difference = 60-25=35
VP
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14 Nov 2005, 16:03
Do we need to consider if total surface area of the new cone does not exceed that of cylindrical tank?
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Director
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14 Nov 2005, 19:24
duttsit,

I am sure ..i just equated the volumes........but i guess checking surface area can be a check!!!!!!!!

duttsit wrote:
Do we need to consider if total surface area of the new cone does not exceed that of cylindrical tank?
Senior Manager
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Re: MGMAT Problem of the week [#permalink]

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15 Nov 2005, 02:52
D for me.
Vol of cyllinder = PI r ^2 h = 1000PI
For scenario1 we get 2000 PI = (1/3)(PI*100*h)
=> h = 60
For scenario 2 we get 2000 PI = (1/3)(PI*r^2*10)
solving for r we get r is approximately 25
So h -r = 35
VP
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21 Nov 2005, 08:18
Good job guys!!
OA is 35.

For OE:
http://www.manhattangmat.com/ChallProbL ... cfm?ID=218
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Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

21 Nov 2005, 08:18
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