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805+ (Hard)|   Geometry|      
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Bunuel
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The figure shown above is a right circular cylinder. The circumferenc 23 Sep 2021, 04:30
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C
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95% (hard)

Question Stats:

47% (03:22) correct 53% (03:17) wrong based on 76 sessions

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The figure shown above is a right circular cylinder. The circumference of each circular base is 20, the length of 𝐴𝐷 is 14, and 𝐴𝐵 and 𝐶𝐷 are diameters of each base respectively. If the cylinder is cut along 𝐴𝐷, opened, and flattened, what is the length of 𝐴𝐶 to the nearest tenth?

A. 16.6
B. 16.8
C. 17.2
D. 17.4
E. 17.6

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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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C
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gloriasc
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The figure shown above is a right circular cylinder. The circumferenc 02 Oct 2021, 03:54
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Can someone explain me how to have the correct answer?
thank you!!!

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NayanikaP
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The figure shown above is a right circular cylinder. The circumferenc 02 Oct 2021, 06:10
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gloriasc
Can someone explain me how to have the correct answer?
thank you!!!

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Hey to answer your question, note that once you cut open the cylinder along AD and open it up, it becomes a rectangle of length 20 Cm (circumference of the circles) and breadth of 14 cm (height of the cylinder).
Once you open it, the point C now becomes the midpoint of the length of the rectangle.
The rest is just applying Pythagorean theorem to find AC with two sides of the triangle being 14 and 10( half of the length of the rectangle)
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ShivangiMittal
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The figure shown above is a right circular cylinder. The circumferenc 01 May 2023, 21:43
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Can someone please explain how they calculated root 74
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Snehaaaaa
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The figure shown above is a right circular cylinder. The circumferenc 28 Jun 2023, 03:46
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Bunuel

The figure shown above is a right circular cylinder. The circumference of each circular base is 20, the length of 𝐴𝐷 is 14, and 𝐴𝐵 and 𝐶𝐷 are diameters of each base respectively. If the cylinder is cut along 𝐴𝐷, opened, and flattened, what is the length of 𝐴𝐶 to the nearest tenth?

A. 16.6
B. 16.8
C. 17.2
D. 17.4
E. 17.6
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Once the cylinder is cut along AD and opened up, it becomes a rectangle with length 20 cm(circumference of the circle becomes the length of rectangle) and height 14cm (height of the cylinder)
On opening the length of the circumference, the points B and C fall at the centre of their respective lengths i.e. the point C now becomes the midpoint of the length of the rectangle.
Now, we have a rectangle with length 10 by height 14 and AC is the diagonal of the rectangle
AC= \(\sqrt{14^2 + 10^2}\)
= \(\sqrt{196 + 100}\)
= \(\sqrt{296}\)
Since, 296 is closest to \(\sqrt{17^2}\)= 289
we understand that AC= something just greater than 17 i.e option C
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stne
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The figure shown above is a right circular cylinder. The circumferenc 29 Jun 2023, 13:18
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gloriasc
Can someone explain me how to have the correct answer?
thank you!!!

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When the cylinder is cut along AD and flattened out, we have something as shown in the fig. below.

Attachment:
GMAT AC.jpg
GMAT AC.jpg [ 9.09 KiB | Viewed 1556 times ]

AC =\( \sqrt{14^2 + 10^2}\)

AC =\( \sqrt{296}\)

AC \(\approx 17\)

Ans = C

Hope it helps.
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