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

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If the circle above has center O and circumference 18m, then the perim [#permalink] New post   Updated on: 21 May 2017, 11:49
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If the circle above has center O and circumference 18π, then the perimeter of sector RSTO Is

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


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6p5jvHu.jpg
6p5jvHu.jpg [ 10.49 KiB | Viewed 25106 times ]
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B

Originally posted by carcass on 21 May 2017, 11:39.
Last edited by Bunuel on 21 May 2017, 11:49, edited 3 times in total.
Edited the question.
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   21 May 2017, 11:48
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carcass wrote:


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

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Show Spoiler
Attachment:
6p5jvHu.jpg


The perimeter of of sector RSTO is (radius OR) + (radius OT) + (minor arc RT).

The circumference is \(18\pi\): \(2\pi{r}=18\pi\) --> \(r=9\);

Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);

So, the perimeter of sector RSTO is (radius OR) + (radius OT) + (minor arc RT) = \(9+9+3\pi=3\pi+18\).

Answer: B.
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If the circle above has center O and circumference 18m, then the perim [#permalink] New post   21 May 2017, 19:06
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carcass wrote:


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

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Show Spoiler
Attachment:
6p5jvHu.jpg


Circumference = 2\(\pi\)r = 18\(\pi\)
r = \(\frac{18}{2}\) = 9

Perimeter of sector RSTO = Arc Length + r + r
Arc Length = 2\(\pi\)r\(\frac{C}{360}\) (C is central angle of the sector)
C = \(60^{\circ}\)
Arc Length = 2\(\pi\)r\(\frac{60}{360}\) = 2*9*\(\pi\)\(\frac{60}{360}\) = 3\(\pi\)

Therefore Perimeter of sector RSTO = 3\(\pi\) + 9 + 9 = 3\(\pi\) + 18
Answer B...

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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   22 May 2017, 13:20
Let's solve it part by part

Arc makes 60 deg i.e. 1/6 of 360 deg that is 1/6 of circumference = π.18/6 = 3.π

Now we know the formula of circumference = π . D where D is diameter
C = π• 18
Observe OR + OT = diameter = 18

Answer B

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

Hence the answer.

B


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If the circle above has center O and circumference 18π, then the perim [#permalink] New post   23 Nov 2017, 15:02
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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

Show Spoiler
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
\(\frac{1}{6}*18π = 3π\)

Radius length?
From circumference:
2πr = 18π
r = 9

Perimeter = (3π + 2*9) = 3π + 18

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

Show Spoiler
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.

Answer: B
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If the circle above has center O and circumference 18m, then the perim [#permalink] New post   04 May 2018, 07:52
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Bunuel what is the concept underneath this line "Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);" Please clarify how you're getting 3pi from 60 degree single angle ROT. Thanks.
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   04 May 2018, 08:06
sadikabid27 wrote:
Bunuel what is the concept underneath this line "Since angle ROT is 60 degrees then minor arc RT is \(\frac{60}{360}*circumference=3\pi\);" Please clarify how you're getting 3pi from 60 degree single angle ROT. Thanks.


Length of arc of the circle is calculated by \(\frac{The Angle Arc Makes With Center}{360}\) * Circumference.

In this case its, \(\frac{60}{360}\)*\(18pi\)= \(3pi\).

Hope its clear.
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   10 Sep 2018, 06:44
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carcass wrote:


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

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Show Spoiler
Attachment:
6p5jvHu.jpg



The circle has circumference 18π
circumference = (2)(radius)(π)
So, (2)(radius)(π) = 18π
Solve to get: radius = 9
So, OR = 9 and OT = 9

Now, we'll deal with arc RST
Here the sector angle = 60°
60°/360° = 1/6
So, the arc RST represents 1/6 of the ENTIRE circle
Since the ENTIRE circle has circumference 18π, the length of arc RST = (1/6)(18π) = 3π

So, the perimeter of sector RSTO = 9 + 9 + 3π
= 18 + 3π

Answer: B
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   14 Sep 2018, 09:30
Expert Reply
carcass wrote:


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

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


Show Spoiler
Attachment:
6p5jvHu.jpg


Since the circumference of circle O is 18π, the radius is 9. Therefore, OR = OT = 9. Furthermore, since angle ROT is 60 degrees, which is 1/6 of 360 degrees, arc RST is 1/6 of the circumference. Therefore, arc RST = 3π. So the perimeter of sector RSTO is 9 + 9 + 3π = 18 + 3π.

Answer: B
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   14 Sep 2018, 11:42
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[quote="carcass"]

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

(A) 3π + 9

(B) 3π + 18

(C) 6π + 9

(D) 6π + 18

(E) 6π + 24


first find the arc,

60/360=x/18π,
x=3π.

then find radius,

2πr=18π,so r=9.
9+9+3π=18+3π. Answer B.
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink] New post   18 Dec 2023, 09:41
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Re: If the circle above has center O and circumference 18m, then the perim [#permalink]
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