Two concentric clrcles are Intercepted by the same central angle.The resulting arc length of the larger circle is 16 m and the radius ofthe larger crcle is 12 m. The radius of the smaller circle corresponding arc ofthe smaller.What’s the length of the corresponding arc of the smaller circle in meters (m)?
Accepted Solution
A:
the correct question in the attached figure
Let A°-----------> the same central angle
For the larger circle length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m
if 360° (full circle) has a length of------------> 75.36 m A°-----------------------------------> 16 m A°=(16)*360/75.36--------> A=76.43°
For the smaller circle length of smaller circle=2pi*r-------> 2*pi*7.5-----> 47.1 m
if 360° (full circle) has a length of------------> 47.1 m 76.43°-----------------------------------> X X=76.43*47.1/360-----> X=10 m ----> length arc of the smaller circle
the answer is the length arc of the smaller circle is 10 m