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What is the farthest distance between two points of a closed

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cloudz9
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What is the farthest distance between two points of a closed [#permalink] New post   04 Jun 2005, 16:41
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)



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Re: What is the farthest distance between two points of a closed [#permalink] New post   04 Jun 2005, 17:07
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.. . :)
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Re: What is the farthest distance between two points of a closed [#permalink] New post   04 Jun 2005, 18:31
I thought E should be 8*sqrt(15) instead of 8*sqrt(5).....I am getting it as 8*sqrt(15)
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Re: What is the farthest distance between two points of a closed [#permalink] New post   04 Jun 2005, 19:06
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? :wink:
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Re: What is the farthest distance between two points of a closed [#permalink] New post   05 Jun 2005, 03:30
2sqrt[257] :shock: :shock: :shock:
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Re: What is the farthest distance between two points of a closed [#permalink] New post   05 Jun 2005, 07:55
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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Re: What is the farthest distance between two points of a closed [#permalink] New post   05 Jun 2005, 12:26
well done!
8 sqrt(5) is right :)



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Re: What is the farthest distance between two points of a closed [#permalink]
05 Jun 2005, 12:26
Moderator:
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