two arcs of concentric circles are intercepted by the same central angle. the resulting arc length of the arc of the larger circ
le is 16 m and the radius of the smaller circle is 7.5 m. find the length of the corresponding arc of the smaller circle
1 answer:
the complete question in the attached figure
Let
A°-----------> <span>the same central angle
</span><span>For the larger circle
length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m
360</span>°<span> (full circle) has a length of------------> 75.36 m
A</span>°-----------------------------------> 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
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
Let
A°-----------> <span>the same central angle
</span><span>For the larger circle
length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m
360</span>°<span> (full circle) has a length of------------> 75.36 m
A</span>°-----------------------------------> 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
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
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