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Difficulty:
15%
(low)
Question Stats:
90% (01:14) correct
10%
(01:52)
wrong
based on 30
sessions
History
Date
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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
Attachment:
2018-11-12_1300.png [ 33.7 KiB | Viewed 2492 times ]
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\(πr^2 = 36π\)
\(r^2\) = 36
r = 6
\(\frac{90}{360}\) = \(\frac{x}{2π6}\)
\(\frac{1}{4}\) = \(\frac{x}{12π}\)
4x = \(12π\)
x = \(3π\) = Arc length ABC
perimeter of sector ABCO = \(3π\)+ Length of OC+ Length of AO
= \(3π\)+6+6
= \(12+3π\)
Answer E
\(r^2\) = 36
r = 6
\(\frac{90}{360}\) = \(\frac{x}{2π6}\)
\(\frac{1}{4}\) = \(\frac{x}{12π}\)
4x = \(12π\)
x = \(3π\) = Arc length ABC
perimeter of sector ABCO = \(3π\)+ Length of OC+ Length of AO
= \(3π\)+6+6
= \(12+3π\)
Answer E
IanStewart
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GMAT Tutor
Joined: 24 Jun 2008
Last visit: 13 Sep 2026
Posts: 4,146
Location: United States
GMAT 1: 780 Q51 V47
Expert reply
GMAT 1: 780 Q51 V47
Posts: 4,146
If the area is 36π, the radius is 6. So the perimeter of the sector will be 6 + 6 + some arclength, so will look like
12 + something with π in it
and E must be right.
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12 + something with π in it
and E must be right.
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now teaching gmat focus
ianstewartgmat.com
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