Final answer:
The area of a sector of a circle with a 4 cm radius and a 30° angle is calculated using the formula A = (θ / 360) × πr², where θ is the central angle in degrees, r is the radius, and π is approximately 3.1415927.
Step-by-step explanation:
The question pertains to finding the area of a sector of a circle, which is a topic in geometry, a branch of Mathematics. The formula for the area of a sector (A) in a circle of radius (r) and central angle (θ) in degrees is given by A = (θ / 360) × πr². In the given question, the radius (r) is 4 cm, and the angle (θ) is 30°. Thus, substituting the values into the formula results in:
A = (30° / 360°) × π × (4 cm)² = (1 / 12) × π × 16 cm² = (π × 16 cm²) / 12
After performing the calculation, the area of the sector can be rounded to the correct number of significant figures based on the measurement precision given in the problem.