A sector of 120 degrees, cut out from a circle, has an area of 66/7 sq cm. Find the radius of the circle?Choices:- 1 CM 2 CM 3 CM 4 CM
Question
A sector of 120 degrees, cut out from a circle, has an area of 66/7 sq cm. Find the radius of the circle?Choices:- 1 CM 2 CM 3 CM 4 CM
Solution
To find the radius of the circle, we first need to understand that the area of the sector is a fraction of the total area of the circle.
The fraction is determined by the ratio of the angle of the sector (120 degrees) to the total angle in a circle (360 degrees).
So, the area of the whole circle is (360/120) * (66/7) = 198/7 sq cm.
The formula for the area of a circle is πr², where r is the radius of the circle.
So, we can set up the equation 198/7 = πr².
Solving for r, we get r = sqrt((198/7)/π) = sqrt(28/π) ≈ 3 cm.
So, the radius of the circle is approximately 3 cm. The closest choice is 3 CM.
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