a circular disc of radius 6cm is divided into three sectors with central angles 90, 120 and 150. what part of the whole circle is the sector with central angle 150 ? also calculate the ratio of the areas of the three sectors.
Answers
Answer:
1-one complete circle has angle 360 degree.
so in 1 degree circle has 1/360part.
and we have asked for 150degree,that's why- 1/360 ×150=5/12part.
2-similarily,we will do for all parts
first we 1/360 ×90=1/4
1/360 ×120=1/3
area of sector when angle=90°
area = πr^2/4
area when angle =120°
area=πr^2/3
area when angle =150°
area=5πr^2/12
now ratio of areas of these sectors will be 1/4 : 1/3 : 5/12
that is 3 : 4 : 5
****radius we are not considering because it will cancelled during finding ratio
Answer:
heyy here is ur answer
Step-by-step explanation:
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