A sector of a circle has an arc length of pi cm and a central angle of pi over 6 radians. What is the area of the sector?
1 answer:
Answer:
Area of sector is 6pi cm^2
Step-by-step explanation:
Mathematically pi radians is 180 degrees
thus pi/6 radians is 180/6 = 30 degrees
The formula for the length of an arc is;
theta/360 * 2 * pi * r
where theta in this case is 30 degrees
And the arc length is pi
so we have
30/360 * 2 * pi * r = pi
30/360 * 2 * r = 1
60r = 360
r = 360/60
r = 6 cm
Now the area of a sector is;
theta/360 * pi * r^2
30/360 * pi * 36
= 6pi cm^2
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