Final answer:
The area of a 30° sector of a circle with an area of 96 m² is 8 m². When expressed in terms of π, the area of the sector is 8π m².
Step-by-step explanation:
The area of a 30° sector of a circle can be found by calculating the fraction of the circle's total area that the sector represents. Since a circle has 360°, a 30° sector covers ⅓ of the whole circle.
Given the circle's total area is 96 m², you would calculate the area of the sector as (30°/360°) × 96 m² = ⅓ × 96 m². Simplifying that gives you 8 m².
However, none of the answer options provided are shown in raw square meters; they are provided in terms of π, where the area of the circle is πr².
So we can express 96 m² in terms of π by setting πr² = 96 m², and solving for r² gives us r² = 96/π.
Now, for the sector, (30°/360°) × (πr²) will give us the area of the sector in terms of π, and since r² = 96/π,
the calculation becomes (1/12) × 96 = 8 m² or 8π m² when expressed using π.