Question

HELP

17) A circle has a radius of 8 centimeters. If the area of a sector is 256pi/3 cm^2, what is the measure of the angle of the sector, in radians?
A) 16pi/3
B) 32pi/3
C) 4pi/3
D) 8pi/3

Answer 1

Explanation:

remember, in radians means we use the arc lengths of the norm circle (radius 1) as angle size.

that means 360° = 2pi

the area of a full circle is

pi×r²

in our case

pi×8² = 64pi

for a segment only a part of 360° or 2pi is used.

so for the area of a sector we have

pi×r² × xpi/2pi

in our case

64pi × xpi/2pi = 256pi/3

32pi × xpi/pi = 256pi/3

32pi × x = 256pi/3

32x = 256/3

x = 8/3

so, the term we need in our sector area calculation is

8pi/3 :

64pi × (8pi/3)/2pi = 256pi/3

so, D is correct.