Radius of circle is 21 cm. What is the central angle subtended by each of the arcs whose length is 110 cm?
2007-08-23 05:00:44 · 4 answers · asked by Booyah! 3 in Science & Mathematics ➔ Mathematics
Radius = 21
Circumference = 132
Arc length = 110
Arc length / Circumference = Central angle / 360
Central angle = 110/132 x 360
The answer is 300 degrees.
2007-08-23 05:06:21 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The central angle has the same numeric measure as the arc it subtends. Circumference of this circle is 3.14(42) = 131.88
the portion of the circle this is is 110/131.88 *360° â 300.27°
2007-08-23 12:14:36 · answer #2 · answered by chasrmck 6 · 0⤊ 0⤋
the length of the arc = alpha*radius
where
alpha = angle (in radians) subtended by the arc
radius = 21cm (given)
so
110 = alpha*21
alpha = 110/21 = 5.238 radians
in degrees, this is 5.238*180/pi = 300 degrees !
This is right because the perimeter of the whole circle is 2piR
= 2pi(21) = 131.9 cm and 110cm is almost that size!
2007-08-23 12:10:33 · answer #3 · answered by vlee1225 6 · 0⤊ 0⤋
x = central angle in radians
21x = 110
x = 5.238 radians = 300.11 degrees
2007-08-23 12:13:39 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋