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# What is the farthest distance between two points of a closed

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Senior Manager
Joined: 17 May 2005
Posts: 273
Location: Auckland, New Zealand
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What is the farthest distance between two points of a closed [#permalink]  04 Jun 2005, 15:41
What is the farthest distance between two points of a closed cylinder with a volume of 512*pi and a surface area of 256*pi?

A) 8*sqrt(3)
B) 8*sqrt(2)
C) 16
D) 8 (2*pi+1)
E) 8*sqrt(5)
Manager
Joined: 07 Mar 2005
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pi * r^2 = 512 pi

2r * pi * h + 2 * pi* r^2 = 256 PI

From the two equations...

r=8
h=8

Draw an imaginary rectangle inside the cylinder to get the farthest two points (the diagnol of the rectagle). 16x16x8

diagnol = sqr(576) = 24

which is not an answer choice.. .
Director
Joined: 18 Feb 2005
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I thought E should be 8*sqrt(15) instead of 8*sqrt(5).....I am getting it as 8*sqrt(15)
Director
Joined: 18 Apr 2005
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Location: Canuckland
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Re: Cylinder [#permalink]  04 Jun 2005, 18:06
cloudz9 wrote:
What is the farthest distance between two points of a closed cylinder with a volume of 512*pi and a surface area of 256*pi?

A) 8*sqrt(3)
B) 8*sqrt(2)
C) 16
D) 8 (2*pi+1)
E) 8*sqrt(5)

height*r^2 = 512
2*r^2 + 2*r*height = 256

the distance is sqrt ( 4r^2 + height^2)

anyone feels like solving a cubic equation with no integer solutions?
Senior Manager
Joined: 19 Feb 2005
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Location: Milan Italy
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2sqrt[257]
Manager
Joined: 07 Mar 2005
Posts: 93
Followers: 1

Kudos [?]: 7 [0], given: 0

Alright, got it.

8sqr(5)

E

raidus = 8
height = 8

Draw a rectangle within the cylinder. The diagnol of the base of the rectangle = 16
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Senior Manager
Joined: 17 May 2005
Posts: 273
Location: Auckland, New Zealand
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well done!
8 sqrt(5) is right
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