If the circle above has center O and an area of
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A. 6π
B. 9π
C. 6 + 3π
D. 9 + 3π
E. 12 + 3π
OA E
Source: Princeton Review
The area is \(36\pi\).BTGmoderatorDC wrote: ↑Thu Oct 22, 2020 7:43 pm2018-11-12_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
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
Area = 36πBTGmoderatorDC wrote: ↑Thu Oct 22, 2020 7:43 pm2018-11-12_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
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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Solution:BTGmoderatorDC wrote: ↑Thu Oct 22, 2020 7:43 pm2018-11-12_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
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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