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# If the circle above has center O and circumference 16π, what the per

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
If the circle above has center O and circumference 16π, what the per  [#permalink]

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04 Apr 2018, 23:51
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15% (low)

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91% (01:20) correct 9% (02:04) wrong based on 32 sessions

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If the circle above has center O and circumference 16π, what the perimeter of sector ABCO?

A. 8+2π

B. 8+4π

C. 8+8π

D. 16+2π

E. 16+4π

Attachment:

45degrees.png [ 8.1 KiB | Viewed 650 times ]

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Re: If the circle above has center O and circumference 16π, what the per  [#permalink]

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05 Apr 2018, 00:27
Circumference = 16pi

2*pi*r* = 16pi

r = 8.

Perimeter of Sector ABCO = 2*r + length of Arc ABC

length of Arc ABC=

45/360 * circumference = circumference/8 =2pi

Hence Perimeter of Sector ABCO = 2*8 +2pi =16+2pi (Answer D)
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Re: If the circle above has center O and circumference 16π, what the per  [#permalink]

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10 Apr 2018, 11:10
Bunuel wrote:

If the circle above has center O and circumference 16π, what the perimeter of sector ABCO?

A. 8+2π

B. 8+4π

C. 8+8π

D. 16+2π

E. 16+4π

Attachment:
45degrees.png

We see that arc ABC is 45/360 = 1/8 of the total circumference of the circle, so the length of arc ABC is 16π x 1/8 = 2π.

Since the diameter of circle O is 16, radii AO and CO are each 8.

Thus, the perimeter of sector ABCO is 2π + 2(8) = 2π +16.

Answer: D
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Re: If the circle above has center O and circumference 16π, what the per   [#permalink] 10 Apr 2018, 11:10
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