find the radius of a circle in which a 62.8 degree central angle cuts off an arc length of 18.4 centimeters
2006-12-15 03:17:10 · 4 answers · asked by Levi M 1 in Science & Mathematics ➔ Mathematics
Circumference formula is 2piR and there are 360 degrees in a circle so:
360/62.8= 5.7324
5.7324*18.4= 105.4777 (total circumference of circle)
2 pi R = 105.4777. Since pi is 3.14159
2 * 3.14159 * R = 105.4777
6.2832 * R = 105.4777
R = 105.4777 / 6.2832
R = 16.7872
2006-12-15 03:31:29 · answer #1 · answered by Scott M 5 · 0⤊ 0⤋
s=theta r.
s is the arc length
theta is the angle in radians
r is the radius
to switch from degrees to radians, multiply by pi/180
62.8 degrees = pi/180
theta = 157 pi/ 450
18.4=157 pi/ 450 r
radius = approx 16.787 centimeters
2006-12-15 03:37:22 · answer #2 · answered by Anonymous · 0⤊ 0⤋
That means letting x be circumference, then 62.8/360 = 18.4/x.
So, x=(360*18.4)/62.8 = 105.4777 approximately.
And since 2pi*r=105.4777, then r=105.4777/(2pi) = 16.787 cm aproximately.
2006-12-15 04:10:13 · answer #3 · answered by yljacktt 5 · 0⤊ 0⤋
length of arc=x/360*2pir
18.4=62.8/360*2*3.14*r
solve for r
2006-12-15 03:22:29 · answer #4 · answered by raj 7 · 0⤊ 0⤋