The area of this circle is 96π m². what is the area of a 30º sector of this circle?

Answer: 8π square meters

Explanation:

First, we convert the angle of the sector to radians, which is 30 degrees.

Note that 180 degrees is equal to π radians. Since 30 degrees is equal to 180 degrees divided by 6,

30 degrees = π/6 radians

Thus, the angle of the sector in radians is π/6.

So, the area of the sector is given by

(Area of sector) = (1/2) (radius) ² (angle of the sector in radians)

= (1/2) (radius) ² (π/6)

= (π/12) (radius) ²

= (1/12) (π) (radius) ²

Note that

(Area of the circle) = (π) (radius) ² = 96π

Therefore, the area of the 30-degree sector is given by

(Area of the sector) = (1/12) (π) (radius) ²

= (1/12) (Area of the circle)

= (1/12) (96π)

(Area of the sector) = 8π square meters