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655-705 (Hard)|   Geometry|      
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Anubhav21
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In the given figure, a regular octagon is shown such that every vertex 08 Aug 2022, 09:31
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C
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55% (hard)

Question Stats:

65% (02:52) correct 35% (02:29) wrong based on 83 sessions

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In the given figure, a regular octagon is shown such that every vertex of the octagon is a center for circular arc and the radius is equal to the side length of the octagon. What is the sum of length of all circular arc, if the side length of the octagon is 1?]

A. 2𝝅
B. 3𝝅
C. 6𝝅
D. 8𝝅
E. 10𝝅
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C

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ThatDudeKnows
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In the given figure, a regular octagon is shown such that every vertex 08 Aug 2022, 14:01
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Anubhav21
In the given figure, a regular octagon is shown such that every vertex of the octagon is a center for circular arc and the radius is equal to the side length of the octagon. What is the sum of length of all circular arc, if the side length of the octagon is 1?]

A. 2𝝅
B. 3𝝅
C. 6𝝅
D. 8𝝅
E. 10𝝅
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There are 8 arcs.
Each arc is \(\frac{3}{8}\) of a circumference.
Each circumference is 2𝝅.

\(8*\frac{3}{8}*2\pi = 6\pi\)

Answer choice C.
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khedikarmohashin
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In the given figure, a regular octagon is shown such that every vertex 13 Aug 2022, 10:02
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3/8 of circumference…..how does it arrives

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dushyant099
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In the given figure, a regular octagon is shown such that every vertex 13 Aug 2022, 12:03
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Hey can you please create picture/ fig of --- that every vertex of the octagon is a center for circular arc and the radius is equal to the side length of the octagon ?
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ThatDudeKnows
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In the given figure, a regular octagon is shown such that every vertex 13 Aug 2022, 12:22
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khedikarmohashin
3/8 of circumference…..how does it arrives

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khedikarmohashin

A circle is 360 degrees. Half a circle is 180 degrees. A quarter of a circle is 90 degrees. An eighth of a circle is 45 degrees. We have a 90 and a 45, so a quarter plus an eighth.

1/4 + 1/8 = 3/8
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samarpan.g28
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In the given figure, a regular octagon is shown such that every vertex 22 Dec 2023, 00:21
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dushyant099
Hey can you please create picture/ fig of --- that every vertex of the octagon is a center for circular arc and the radius is equal to the side length of the octagon ?
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To find the interior angles of a regular polygon, use this formula: theta = {(n-2)*180}/n. For the octagon, n=8 thus from the formula we get theta = 135.
Now, to find the total of 8 arcs, 8*(theta/360)*circumference, or 8*(135/360)*2*pi*1 = 6*pi. This is the answer.
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