If the circle above has center O and an area of

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Oct 22, 2020 7:43 pm

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If the circle above has center O and an area of 36π, what is the perimeter of sector ABCO ?

A. 6π
B. 9π
C. 6 + 3π
D. 9 + 3π
E. 12 + 3π

OA E

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Oct 22, 2020 7:43 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If the circle above has center O and an area of

by swerve » Fri Oct 23, 2020 4:11 pm

BTGmoderatorDC wrote: ↑
Thu Oct 22, 2020 7:43 pm
2018-11-12_1300.png

If the circle above has center O and an area of 36π, what is the perimeter of sector ABCO ?

A. 6π
B. 9π
C. 6 + 3π
D. 9 + 3π
E. 12 + 3π

OA E

Source: Princeton Review

The area is $36\pi$.

So $r^2 = 36$ and $r = 6$

The total circumference of the circle is $12\pi$ out of which we are interested in $1/4$th part, so curved perimeter is $3pi$. Plus the region $ABCO$ also has two radii of straight lines

Hence perimeter is $12 + 3\pi \Longrightarrow$ E

jhavyom: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Oct 02, 2020 9:16 am

Re: If the circle above has center O and an area of

by jhavyom » Sun Nov 01, 2020 2:44 am

BTGmoderatorDC wrote: ↑
Thu Oct 22, 2020 7:43 pm
2018-11-12_1300.png

If the circle above has center O and an area of 36π, what is the perimeter of sector ABCO ?

A. 6π
B. 9π
C. 6 + 3π
D. 9 + 3π
E. 12 + 3π

OA E

Source: Princeton Review

Area = 36π
πr^2 = 36π
r^2 = 36
r = 6

ABCO Perimieter = πr/2 + 2r
= (6/2)π + 2*6
= 3π + 12

Option E is the answer.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If the circle above has center O and an area of

by Scott@TargetTestPrep » Thu Nov 12, 2020 7:34 am

BTGmoderatorDC wrote: ↑
Thu Oct 22, 2020 7:43 pm
2018-11-12_1300.png

If the circle above has center O and an area of 36π, what is the perimeter of sector ABCO ?

A. 6π
B. 9π
C. 6 + 3π
D. 9 + 3π
E. 12 + 3π

OA E

Solution:

We see that the perimeter of sector ABCO consists of radii AO and CO and arc ABC.

Since the area of the circle is 36π, the radius of the circle is 6. So AO = CO = 6. Since angle AOC is 90 degrees, then arc ABC is 1/4 of the circumference of the circle. Since the circumference of the circle is 2 x 6 x π = 12π, then arc ABC is 1/4 x 12π = 3π. Therefore, the perimeter of sector ABCO is 6 + 6 + 3π = 12 + 3π.

Answer: E

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