Question:
a circular disc of 6 cm of radius divided into three sections with central angles 120 degrees, 150 degrees and 90 degrees. what part of the circle is the sector with the central angle as 120 degrees . also find the ratio of the areas of three sectors.
Answer:
Given, radius of the circular disc = 6 cm
1. Now when θ = 120,
then area of the sector = (θ/360)* πr2
= (120/360)* πr2
= πr2 /3
So, (1/3)rd part of the circle is the sector with the central angle as 120 degrees.
2. Now, when θ = 150
then area of the sector = (θ/360)* πr2
= (150/360)* πr2
= (15/36)* πr2
= (5/12)* πr2
Now, when θ = 90
then area of the sector = (θ/360)* πr2
= (90/360)* πr2
= πr2 /4
Now, ratio = πr2 /3 : 5πr2 /12 : πr2 /4
= 1/3 : 5/12 : 1/4
= 4 : 5: 3
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