if an arc of a circle is 135 degrees & the length is 9 cm, what is the length of the radius of this circle? round your answer to 2 decimal places.
2007-03-05 05:11:47 · 6 answers · asked by JoAnna 2 in Science & Mathematics ➔ Mathematics
radius
= (9*360)/(135*2*3.14)
= 12/3.14
= 1200/314
= 3.82cm
2007-03-05 05:21:06 · answer #1 · answered by ganesan 2 · 0⤊ 0⤋
I would change the degrees to radian
135 deg = 135(pi)/180 radians
the arc length is equal to the radius times the included angle
therefor 9 = radius(135pi/180)
9(180)/(135pi) = radius = 3.82 cm
2007-03-05 13:28:49 · answer #2 · answered by bignose68 4 · 0⤊ 0⤋
Length of an arc of a circle = radius x angle in radians.
Thus 9 cm = R x 135xpi/180= Rx (3/4)pi
Therefore R = 9/(0.75x3.141) = 3.82 cm
2007-03-05 13:21:42 · answer #3 · answered by physicist 4 · 1⤊ 0⤋
Suppose the arc was 360°. Then you would haver the whole circunference of length:
2ÏR
But you have an arc only of 135°. Which is 135/360 of the whole circle.
2ÏR*(135/360) and this equals 9cm
2ÏR*0.375 = 9
Solving for R you get
R = 9 / (2Ï*0.375 ) = 3.82 cm approximately.
.
2007-03-05 13:21:31 · answer #4 · answered by Ferts 3 · 0⤊ 0⤋
the length of an arc of135 deg is
L=2pi*r *135/360 =9
r= 9*360/(2pi*135) =3.82cm
2007-03-05 13:25:05 · answer #5 · answered by santmann2002 7 · 0⤊ 0⤋
First find the circumference. Then divide by 2Ï to get the radius.
c = (360/135)(9)
r = c/(2Ï) = (360/135)(9)/(2Ï) = (9*360)/(2*135*Ï)
r = (9*360)/(270Ï) = (9*4)/(3Ï) = 3*4/Ï
r = 12/Ï â 3.82 cm
2007-03-06 02:35:17 · answer #6 · answered by Northstar 7 · 0⤊ 0⤋