PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)...

To find the area of the sector PQR, we need to know the angle at the center of the circle that the sector subtends. Since the radius of the circle is 4 cm and PQR = 30^o, the circumference of the circle is 2πr = 8π cm. The fraction of the circle that the sector PQR subtends is 30/360, or 1/12. Therefore, the area of the sector PQR is 1/12 of the total area of the circle: Area of sector PQR = (1/12) × πr² = (1/12) × π × (4 cm)² ≈ 3.347 cm² Rounded to 3 significant figures, the area of sector PQR is approximately 3.35 cm², which corresponds to the first option: 4.19 cm².