Final answer:
The area of the smaller sector is approximately 9.42 square inches. So, Area of smaller sector with a 30-degree angle and 6-inch radius is (1/12)π(36) ≈ 9.42 square inches.
Step-by-step explanation:
To find the area of a sector, we use the formula:
A = (θ/360) * π * r²
where A is the area, θ is the angle of the sector, and r is the radius.
Given that the angle is 30 degrees and the radius is 6 inches, we can substitute these values into the formula:
A = (30/360) * π * 6²
Simplifying the equation, we get:
A = (1/12) * π * 36
A = 3π square inches
So, the area of the smaller sector is approximately 9.42 square inches.
To find the area of the smaller sector, you can use the formula for the area of a sector: A = (θ/360)πr², where θ is the central angle and r is the radius. In this case, with an angle of 30 degrees and a radius of 6 inches, substitute these values into the formula. A = (30/360)×π×(6)² simplifies to (1/12)×π×(36), resulting in an area of 3π square inches. Therefore, the area of the smaller sector is approximately 9.42 square inches, providing a measure of the region enclosed by the 30-degree angle and the given radius.