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555-605 (Medium)|   Geometry|      
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Bunuel
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A circular field that measures 100π meters in circumference has six mo 23 Jan 2015, 07:29
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C
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25% (medium)

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79% (01:53) correct 21% (02:27) wrong based on 157 sessions

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A circular field that measures 100π meters in circumference has six monuments evenly spaced around that circumference. If a hexagonal path has been installed to allow patrons to walk straight from monument to as pictured, what is the length, in meters, of that path.

A. 240
B. 270
C. 300
D. 330
E. 360

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monuments.png
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C
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A circular field that measures 100π meters in circumference has six mo 23 Jan 2015, 07:33
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ans C 300...
each sector is of 60 degree...
which makes it eq triangle.. so each side is 50 which ir radius found from circumference.
ans 50*6=300
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A circular field that measures 100π meters in circumference has six mo 23 Jan 2015, 07:55
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6 equilateral triangles with side 50 units......(2 pi r = 100)

So path length - 50*6 = 300
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A circular field that measures 100π meters in circumference has six mo 26 Jan 2015, 04:26
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Bunuel

A circular field that measures 100π meters in circumference has six monuments evenly spaced around that circumference. If a hexagonal path has been installed to allow patrons to walk straight from monument to as pictured, what is the length, in meters, of that path.

A. 240
B. 270
C. 300
D. 330
E. 360

Show Spoiler
Attachment:
monuments.png
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VERITAS PREP OFFICIAL SOLUTION:

The key to solving this question is recognizing that, with six equally spaced items around a circle, the lines connecting the center of the circle to each item will form 60-degree angles (each pair of adjacent lines will form a 1/6 section of the circle). That means that, since you know the circumference of the circle is 100π the radius is 50. And what you're really looking to calculate - the distance from each monument to the next - will then form a set of equilateral triangles with all sides 50. Each monument-to-monument distance will form the third side of an isosceles triangle (each radius is the same) with one angle 60, so they must all be equilateral.

Therefore, the straight-line distance from each monument to the next will be 50, and with six such distances forming the path, the path will total 300 meters in length.

Answer: C.
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A circular field that measures 100π meters in circumference has six mo 03 Feb 2015, 00:53
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Answer = C. 300

Attachment:
monuments.png
monuments.png [ 8.28 KiB | Viewed 5137 times ]

Six equilateral triangles formed with each side = radius of circle \(= \frac{100\pi}{2\pi} = 50\)

Total length of path = 6*50 = 300
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