I have a circle with a radius of 6 units and a central angle of 33 degrees. How would I find the intercepted arc length and the area of that segment?
2007-10-11 18:08:11 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
C = 2πr
C = 12π units
Length of arc
(33 / 360) x 12π units
3.46 units
Area of circle = π 6² units ²
Area of segment
(33 / 360) x 36π units ²
10.4 units ² (to 1 decimal place)
2007-10-12 07:52:54 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Long time since I've worked trig but here is a guess:
A circle has 360 degrees. 33 degrees is 33/360 of a circle.
The area of a circle is pi times radius squared.
Substituting: Aof your segment = 33/360 times 6^2
or 33/360 times 36
33/10 or 3.3 = area of segment.
The circumference of a circle is pi times diameter.
If your radius is 6 units then the diameter is 2 times the radius or 12 units. The circumference of the entire circle is pi times 12. The arc length of your segment is 33/360 times 12 or
33/30 = 1.1 units
2007-10-12 01:29:38 · answer #2 · answered by duffy 4 · 0⤊ 0⤋