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# What is the longest possible distance between any two points on a cyli

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the longest possible distance between any two points on a cyli  [#permalink]

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02 Sep 2018, 21:51
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Difficulty:

35% (medium)

Question Stats:

71% (00:41) correct 29% (00:36) wrong based on 22 sessions

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What is the longest possible distance between any two points on a cylinder with radius 6?

(1) The diameter of the cylinder is equal to its height.
(2) The area of the base is 36π.

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Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: What is the longest possible distance between any two points on a cyli  [#permalink]

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02 Sep 2018, 22:13
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Bunuel wrote:
What is the longest possible distance between any two points on a cylinder with radius 6?

(1) The diameter of the cylinder is equal to its height.
(2) The area of the base is 36π.

the longest distance is diagonal as shown in the sketch. So we require diameter and height to find the diagonal..
we know radius is 6, so we require to know height.

let us see the statements..

(1) The diameter of the cylinder is equal to its height.
So height = 2r=2*6=12
hence the distance = $$\sqrt{dia^2+height^2}=\sqrt{12^2+12^2}=12\sqrt{2}$$
sufficient

(2) The area of the base is 36π.
insuff

A
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Re: What is the longest possible distance between any two points on a cyli   [#permalink] 02 Sep 2018, 22:13
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