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

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