SOLUTION: You have a sector PQR where QR is the arc of the circle with center P. If the lenght of the arc QR is 6pi, and the angle formed at point P is 30 degrees, what is the area of the se

Question 467135: You have a sector PQR where QR is the arc of the circle with center P. If the lenght of the arc QR is 6pi, and the angle formed at point P is 30 degrees, what is the area of the sector PQR?
The answer is 108pi.
I do not understand how they got this answer.
Can you help?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: 30 degrees = radians

Arc length: where is the central angle (that subtends, ie cuts, the arc....this angle is in radians) and r is is the radius

So we're given that and . So

which means that the radius of this circle is 36 units.

Area of sector:

plug in and

So the area is
RELATED QUESTIONS
QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree (answered by Big Poop)

QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree... (answered by Big Poop,TutorDelphia)

QR is an arc of a circle with a center P. If the length of the arc is 6pi and the degree... (answered by )

P, Q and R are three points on a circle. If the ratio of arc pq:qr:pr = 3:4:5, find the... (answered by Fombitz)

Triangle PQR has PQ=8cm, QR= 10cm and angle PQR is 40�. Calculate the area of triangle... (answered by stanbon)

Circles M and K are congruent, arc QR is congruent to arc LN . Find the length of (answered by MathLover1)

If measurement angle P is 40 and measurement Arc QR is 86 , find measurement arc... (answered by stanbon)

Find the area of the sector of a circle if r = 4 and the measure of the arc is 60�. (answered by richard1234)

A sector of a circle has an arc length of π cm and a central angle of π/6 radians. What (answered by josgarithmetic,MathTherapy)