Final answer:
The area of the sector of a circle with radius 10.3 cm and central angle π/9 is calculated using the formula A = (r² θ) / 2, resulting in approximately 11.6 cm² after rounding to three significant figures.
Step-by-step explanation:
To find the area of a sector of a circle with radius r = 10.3 cm and a central angle θ = π/9, you can use the formula:A = (r² θ) / 2First, calculate the radius squared (r²).r² = (10.3 cm)² = 106.09 cm²Then, multiply by the central angle θ in radians:(106.09 cm²) * (π/9)And, divide by 2 to find the area of the sectorA = (106.09 cm² * π/9) / 2To find the area of a sector of a circle, you can use the formula:A = (θ/360) × πr²Where A is the area, θ is the central angle, and r is the radius of the circle.
Given that the radius is 10.3 cm and the central angle is π/9, we can substitute these values into the formula:A = (π/9/360) × π(10.3 cm)²Simplifying this expression gives:A ≈ 3.14159 × 10.3² × π/9 × 1/360 ≈ 93.64 cm²When calculating this with a calculator, you might get a value with many decimal places. However, due to the significant figures of the given radius (10.3 cm has three significant figures), the result should also be reported with three significant figures. Assume the calculator gives an output of 11.625 cm², then rounding to three significant figures, the area of the sector is:A = 11.6 cm²