Question

The two sectors of a circle have the central angles as 1200 and 1500 respectively. Then the find the ratio between the areas of the two sectors

Answer 1

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

Answer 2

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