Question

a circle is divided into 6 sectors in such a way that the angles of the sector are in arithmetic progression. the angle of the largest sector is 4 times the angle of the smallest sector. Given that the radius of the circle is 5cm. Calculate the perimeter of the smallest sector

Answer 1

Sum of AP = n(a1 + an)/2. n = 6 (Given)
Let a1 = x, then an = 4x
Therefore sum = 360° = 6/2*(x + 4x)
⇒ 5x = 360/3 ⇒ x = 120/5 = 24°
The perimeter of the smallest sector, given by S + 2r
S = rФ = 5cm*24° = 5*0.418879rads = 2.094 cm.
∴ The perimeter of the sector = 2.094+5+5 = 12.094cm.