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

Question

https://gmatclub.com/forum/download/file.php?id=35366 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 6p5jvHu.jpg

Bunuel · Accepted Answer

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.

sashiim20 · Answer

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... _________________ Kindly press "+1 Kudos" to appreciate

irishiraj87 · Answer

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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RicAssassin · Answer

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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generis · Answer

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

JeffTargetTestPrep · Answer

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

sadikabid27 · Answer

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.

seed · Answer

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.

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

abhishekdadarwal2009 · Answer

https://gmatclub.com/forum/download/file.php?id=35366

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.

bumpbot · Answer

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

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