the circumference of circle is divided into six arc such that they form an a.p and ratio of smallest and largest arc is 1/5 then find angle between 1st and 2nd arc?
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Step-by-step explanation:
First you need to find the size of the smallest angle.
Let the smallest angle be x°
Therefore the largest angle is 4x°
You know the size of the first and sixth (last) sectors and that the sum of all the sectors in the circle is 360°
Sn=n2(a+l) ← sum of the terms in an AP
S6=62(x+4x)=360°
3(5x)=360°
5x=120°
x=24°
The smallest sector is therefore 24360=115 of the circle.
The perimeter is made up of 2 radii and an arc.
The length of the arc is fraction×circumference
Arc length = 115×2π(5) ←(C=2πr)
=23π
Perimeter =5+5+23π
=12.09cm
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