If the circle above has center O and an area of

[BTGmoderatorDC]

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

[swerve]

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]

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.

[Scott@TargetTestPrep]

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