To find the area of a 30-degree sector of a circle with a total area of 96π m², we first need to understand how to calculate the area of a sector based on the angle it encompasses.
The formula to find the area of a sector is:
Area of Sector = (θ / 360) × Total Area of Circle
In this formula, θ represents the angle of the sector in degrees. For our problem, the total area of the circle is given as 96π m² and the angle of the sector is 30 degrees.
Now, let’s plug in the values:
Area of Sector = (30 / 360) × 96π
First, simplify the fraction:
Area of Sector = (1 / 12) × 96π
Now, multiply:
Area of Sector = 96π / 12 = 8π
Thus, the area of the 30-degree sector of this circle is 8π m².
This means if you were to slice out a 30-degree piece of this circle, it would cover an area of 8π m², which gives you an idea of how much space that section occupies in comparison to the total area of the circle.