If the area of a sector of a circle is 8π and with central angle 45 degrees, what is the radius of the circle?

Question

If the area of a sector of a circle is 8π and with central angle 45 degrees, what is the radius of the circle?

a) 4 b) 8 c) 16 d) 64

Answer 1

Area of a circle is pir^2. Area of a sector with central angle 45 degrees is 1/8 of the circle's area

or (1/8)pir^2 = 8pi. divide by pi (cancel the pi on both sides) to get r^2/8 = 8. r^2 = 64, r= 8

b) is correct

if the central angle had been 180 degrees, the sector's area would have been half the circle's area

if the central angle had been 90 degrees, the sector's area would be 1/4 of the circle's area

with 45 degrees, the sector's area is 1/8 of the circle's area