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# What is the greatest distance between any two points on a cylinder wit

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Math Expert
Joined: 02 Sep 2009
Posts: 55267
What is the greatest distance between any two points on a cylinder wit  [#permalink]

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10 Apr 2018, 04:01
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Difficulty:

25% (medium)

Question Stats:

81% (01:01) correct 19% (00:58) wrong based on 40 sessions

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What is the greatest distance between any two points on a cylinder with radius 3 and height 8?

A. √73

B. √80

C. 9

D. √91

E. 10

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Joined: 14 Feb 2018
Posts: 390
Re: What is the greatest distance between any two points on a cylinder wit  [#permalink]

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10 Apr 2018, 04:08
The greatest distance will be that from one corner of the cylinder to the exact opposite (diagonally).

√(8^2 + (3+3)^2) = √(64 + 36) = √100 = 10.

Hence option E.

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Joined: 04 Apr 2018
Posts: 21
Re: What is the greatest distance between any two points on a cylinder wit  [#permalink]

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10 Apr 2018, 05:23
For the sake of easy calculations, let's say the 3D object has a projected shadow on a wall. That shadow would be a rectangle & the greatest distance would be the diagonal of this rectangle. And the calculation is pretty much simple as both sides of triangle are (6,8) which is a right angled triangle triplet with 10. Hence, E.

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Re: What is the greatest distance between any two points on a cylinder wit  [#permalink]

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11 Apr 2018, 16:17
Bunuel wrote:
What is the greatest distance between any two points on a cylinder with radius 3 and height 8?

A. √73

B. √80

C. 9

D. √91

E. 10

The greatest distance in a cylinder will be the diagonal from the top left to the bottom right. This diagonal, along with the height of the cylinder and the diameter of the circular base, will form a right triangle with the height and the diameter being the legs and the diagonal being the hypotenuse. We see the two legs of the diagonal are 6 (diameter) and 8 (height). So the hypotenuse of the right triangle, or the diagonal, will be 10.

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Re: What is the greatest distance between any two points on a cylinder wit   [#permalink] 11 Apr 2018, 16:17
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