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

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A cylindrical tank, with radius and height both of 10 feet, [#permalink] New post 14 Nov 2005, 13:09
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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 [#permalink] New post 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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 [#permalink] New post 14 Nov 2005, 14:34
D

1 ) Radius same
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
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 [#permalink] New post 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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 [#permalink] New post 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?
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Re: MGMAT Problem of the week [#permalink] New post 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
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 [#permalink] New post 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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  [#permalink] 21 Nov 2005, 08:18
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