A circle has a sector with area 1/2 pie and central angle of 1/9 pie radians what is the area of the circle?

Answer 1

The area of a sector of a circle is (1/2)r²θ, where r is the radius and θ is the radian measure of the central angle of the sector.

So, we have (1/2)r²(π/9) = π/2. Therefore, r² = 9, so r = 3.

Area of circle = πr² = 9π.

Answer 2

The area of a sector of a circle is A_sector=(x/360)πr², where "x" is the central angle of the sector in degrees. The area of a circle is A=πr². We are given that the central angle is (1/9)π radians.

π (radians) = 180 (degrees)

(1/9)π = (1/9)(180) = 20° = x

A_sector = (1/2)π = (20/360)πr²

(1/2)π = (1/18)πr² substitute values for area and "x"

18(1/2) = r² multiply both sides by 18π to isolate r²

9 = r² simplify

r = ±3 square both sides

r = 3 radius cannot be negative

Using this value of "r", we can solve for the total area of the circle.

A = πr²

A = (3)²π

A = 9π

Hope this helps!