Discussion
In the figure shown, O is the center of the circle. If the area of the circle is 9π, then the perimeter of the sector PRQO is
*This question is included in Nova Math - Problem Set J: Geometry, question #20
| (A) |  – 6 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 07/20/2012 19:42
Where does the +6 come from?
Posted: 07/20/2012 20:15
Since the area of the circle is 9π, we get
πr^2 = 9π
r^2 = 9
r = 3
Now, the circumference of the circle is
C = 2πr = 2π3 = 6π
Since the central angle is 30°, the length of arc PRQ is 30° / 360° or 1/12·6π or π/2.
BUT, the perimeter of the section includes OP and OQ, which is just the radius.
So you have to add 3 + 3 to π/2.
πr^2 = 9π
r^2 = 9
r = 3
Now, the circumference of the circle is
C = 2πr = 2π3 = 6π
Since the central angle is 30°, the length of arc PRQ is 30° / 360° or 1/12·6π or π/2.
BUT, the perimeter of the section includes OP and OQ, which is just the radius.
So you have to add 3 + 3 to π/2.
Posted: 07/20/2012 20:59
I swear my brain is melting! Thanks for pulling me back into reality.