Question

A circle has a radius of 6 inches.
Find the area of a sector of this circle that is intercepted by a central angle measuring 30°.
2π
3π
6π
12π

Answer 1

nice question again!! :)

A central angle is measured by its intercepted arc.
Let's denote the length of the intercepted arc with s, and the length of the radius r. So,
s = 6 cm and r = 30 cm.
When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian.
To find the angle in our problem we use the following relationship:
measure of an angle in radians = (length of the intercepted arc)/(length of the radius)
measure of our angle = s/r = 6/30 = 1/5 radians.
Now, we need to convert this measure angle in radians to degrees.
Since pi radians = 180 degrees, then
1 radians = 180/pi degrees, so:
1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.

Answer 2

so 6

Answer 3

Thirty degrees is one twelfth of the disk, so find the area of the disk and divide by twelve. By mental math, I think the answer is about 3 pi.