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# If the circle above has center O and circumference 18π, then the perim

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Math Expert
Joined: 02 Sep 2009
Posts: 46051
If the circle above has center O and circumference 18π, then the perim [#permalink]

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21 Nov 2017, 23:16
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Difficulty:

15% (low)

Question Stats:

89% (00:45) correct 11% (00:36) wrong based on 38 sessions

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If the circle above has center O and circumference 18π, then the perimeter of the sector RST is

(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24

Attachment:

2017-11-21_1032_002.png [ 7.12 KiB | Viewed 646 times ]

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Re: If the circle above has center O and circumference 18π, then the perim [#permalink]

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22 Nov 2017, 05:44
Answer is B. 3*pi + 18.

We can find the radius from the circumference which is equal to 2*pi*r.

And the length of the arc is (Angle/360) X Circumference.

B

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If the circle above has center O and circumference 18π, then the perim [#permalink]

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23 Nov 2017, 15:02
Bunuel wrote:

If the circle above has center O and circumference 18π, then the perimeter of the sector RST is

(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24

Attachment:
2017-11-21_1032_002.png

Perimeter of sector RST =
RST arc length + 2*(radius)

Sector RST is what fraction of the circle?

$$\frac{SectorAngle}{Circle}=\frac{60°}{360°}=\frac{1}{6}$$

Sector RST = $$\frac{1}{6}$$ of the circle.

RST arc length?
$$\frac{1}{6}$$ of circumference
$$\frac{1}{6}*18π = 3π$$

From circumference:
2πr = 18π
r = 9

Perimeter = (3π + 2*9) = 3π + 18

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Re: If the circle above has center O and circumference 18π, then the perim [#permalink]

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27 Nov 2017, 12:25
Bunuel wrote:

If the circle above has center O and circumference 18π, then the perimeter of the sector RST is

(A) 3π + 9
(B) 3π + 18
(C) 6π + 9
(D) 6π + 18
(E) 6π + 24

Attachment:
2017-11-21_1032_002.png

We see that arc RST corresponds with a central angle of 60 degrees; thus, arc RST is 60/360 = 1/6 of the circumference of the circle. Thus, arc RST = ⅙ x 18π = 3π.

Since the circumference = 18π, the radius of the circle = 18π/(2π) = 9. We see that RO and TO are radii, so each is equal to 9.

Thus, the perimeter of sector RST is 3π + 9 + 9 = 3π + 18.

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Re: If the circle above has center O and circumference 18π, then the perim   [#permalink] 27 Nov 2017, 12:25
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# If the circle above has center O and circumference 18π, then the perim

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