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# The figure above represents a right circular cylindrical tube made out

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139576 [1], given: 12794

The figure above represents a right circular cylindrical tube made out [#permalink]

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08 Dec 2017, 02:46
1
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Expert's post
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Difficulty:

75% (hard)

Question Stats:

32% (01:06) correct 68% (05:26) wrong based on 56 sessions

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The figure above represents a right circular cylindrical tube made out of paper. The circumference of each circular base is 10 centimeters, the length of AB is 12 centimeters, and BD is a diameter of a base. If the tube is cut along AB, opened and flattened, what is the length of AD in centimeters?

(A) 13
(B) 17
(C) 22
(D) 2√61
(E) √146.5

[Reveal] Spoiler:
Attachment:

2017-12-08_1440_002.png [ 6.2 KiB | Viewed 661 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 139576 [1], given: 12794

Director
Joined: 18 Aug 2016
Posts: 627

Kudos [?]: 208 [0], given: 167

Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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08 Dec 2017, 03:01
Bunuel wrote:

The figure above represents a right circular cylindrical tube made out of paper. The circumference of each circular base is 10 centimeters, the length of AB is 12 centimeters, and BD is a diameter of a base. If the tube is cut along AB, opened and flattened, what is the length of AD in centimeters?

(A) 13
(B) 17
(C) 22
(D) 2√61
(E) √146.5

[Reveal] Spoiler:
Attachment:
2017-12-08_1440_002.png

2*pie * r = 10
r = 5/pie
ABD will be right angle Triangle
AD is Hypotenuse and hence can be calculated
AD = $$\sqrt{(12^2 + (5/pie)^2)}$$
AD = $$\sqrt{(144 + 25/~9.5)} = \sqrt{146.5}$$
E
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Kudos [?]: 208 [0], given: 167

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Joined: 24 Nov 2016
Posts: 151

Kudos [?]: 31 [1], given: 40

Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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08 Dec 2017, 05:44
1
KUDOS
Bunuel wrote:

The figure above represents a right circular cylindrical tube made out of paper. The circumference of each circular base is 10 centimeters, the length of AB is 12 centimeters, and BD is a diameter of a base. If the tube is cut along AB, opened and flattened, what is the length of AD in centimeters?

(A) 13
(B) 17
(C) 22
(D) 2√61
(E) √146.5

[Reveal] Spoiler:
Attachment:
2017-12-08_1440_002.png

If the tube is opened and flattened, then we have a rectangle with length 12 = AB, and width 10 = the circumference.

Now, lines BD and AC are equal to half the width = 10/2 = 5.

So to find the distance AD, we need to find the diagonal of the rectangle with length 12 = AB and width 5 = BD

$$a^2+b^2=c^2, 12^2+5^2=c^2, 169=c^2, c=13$$

(A) is the answer.

Last edited by exc4libur on 09 Dec 2017, 08:06, edited 1 time in total.

Kudos [?]: 31 [1], given: 40

Veritas Prep GMAT Instructor
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Location: Pune, India
Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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08 Dec 2017, 06:15
2
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Expert's post
Bunuel wrote:

The figure above represents a right circular cylindrical tube made out of paper. The circumference of each circular base is 10 centimeters, the length of AB is 12 centimeters, and BD is a diameter of a base. If the tube is cut along AB, opened and flattened, what is the length of AD in centimeters?

(A) 13
(B) 17
(C) 22
(D) 2√61
(E) √146.5

[Reveal] Spoiler:
Attachment:
2017-12-08_1440_002.png

When you cut along AB and open it, you get a rectangle. Notice that in this rectangle, A is on the corner and D is in the centre of the opposite edge. So ABD will form a right triangle.

AB^2 + BD^2 = AD^2

AB is simply the length of the tube at 12 cm but notice what BD is. It is half the circumference of the circular base (since it is opened and flattened) which is 10 cm. So BD = 10/2 = 5 cm

This will be a 5-12-13 triangle then and AD will be 13 cm.

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18488 [2], given: 237 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7868 Kudos [?]: 18488 [1], given: 237 Location: Pune, India Re: The figure above represents a right circular cylindrical tube made out [#permalink] ### Show Tags 08 Dec 2017, 20:15 1 This post received KUDOS Expert's post VeritasPrepKarishma wrote: Bunuel wrote: The figure above represents a right circular cylindrical tube made out of paper. The circumference of each circular base is 10 centimeters, the length of AB is 12 centimeters, and BD is a diameter of a base. If the tube is cut along AB, opened and flattened, what is the length of AD in centimeters? (A) 13 (B) 17 (C) 22 (D) 2√61 (E) √146.5 [Reveal] Spoiler: Attachment: The attachment 2017-12-08_1440_002.png is no longer available When you cut along AB and open it, you get a rectangle. Notice that in this rectangle, A is on the corner and D is in the centre of the opposite edge. So ABD will form a right triangle. AB^2 + BD^2 = AD^2 AB is simply the length of the tube at 12 cm but notice what BD is. It is half the circumference of the circular base (since it is opened and flattened) which is 10 cm. So BD = 10/2 = 5 cm This will be a 5-12-13 triangle then and AD will be 13 cm. Answer (A) Responding to a pm: Quote: Can you help me understand how BD is half the circumference of the circular base. I am unable to visualize and hence not getting the point. Here is the original roll. Attachment: Rectangular Roll Original.jpg [ 11.96 KiB | Viewed 395 times ] When you open it, this is what it looks like. Attachment: Rectangular Roll.jpg [ 14.09 KiB | Viewed 395 times ] _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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22 Dec 2017, 05:48
1
KUDOS
Got the answer to be A

Can anyone explain how it is D??

Kudos [?]: 1 [1], given: 215

Math Expert
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139576 [1], given: 12794

Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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22 Dec 2017, 05:57
1
KUDOS
Expert's post
MSarmah wrote:
Got the answer to be A

Can anyone explain how it is D??

The correct answer is A. Edited. Thank you.
_________________

Kudos [?]: 139576 [1], given: 12794

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Joined: 19 Aug 2017
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Re: The figure above represents a right circular cylindrical tube made out [#permalink]

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22 Dec 2017, 06:06
Bunuel wrote:
MSarmah wrote:
Got the answer to be A

Can anyone explain how it is D??

The correct answer is A. Edited. Thank you.

Welcome Brunnel

Kudos [?]: 1 [0], given: 215

Re: The figure above represents a right circular cylindrical tube made out   [#permalink] 22 Dec 2017, 06:06
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# The figure above represents a right circular cylindrical tube made out

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