A circle is divided into 6 sectors so that the angles of the sectors form an arithmetic progression. The largest sector angle is 4 times the smallest sector angle. Given that the radius of the circle is 5cm find the perimeter of smallest sector?

1 Answer
Dec 7, 2017

#=12.09 cm#

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°#

#S_n = n/2(a+l) " "larr# sum of the terms in an AP

#S_6 = 6/2(x+4x)= 360°#

#3(5x)=360°#

#5x=120°#

#x=24°#

The smallest sector is therefore #24/360 = 1/15# of the circle.

The perimeter is made up of #2# radii and an arc.

The length of the arc is #"fraction" xx "circumference"#

Arc length = #1/15 xx 2pi(5)" "larr (C=2pi r)#

#=2/3pi#

Perimeter #= 5+5+2/3pi#

#=12.09 cm#

This is a really nice question which includes different topics in Maths!!