Question

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.​

Answer 1

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 2

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