Final answer:
The areas and arc lengths of the sectors are calculated using the sector area formula (½ r2θ) and the arc length formula (rθ), converting the central angles to radians first.
Step-by-step explanation:
The areas of sectors in a circle are calculated using the formula ½ r2θ, where r is the radius of the circle and θ is the central angle in radians. The lengths of the arcs are calculated using the formula rθ, where θ is in radians. For the circle with radius 7 cm and central angle 120°, the area of the sector is ½ × 72 × (π/180 × 120) = ½ × 49 × (π/3) cm2. The length of the arc is 7 × (π/180 × 120) = 7 × (π/3) cm.
For the circle with radius 21 cm and central angle 40°, the area of the sector is ½ × 212 × (π/180 × 40) = ½ × 441 × (π/9) cm2. The length of the arc is 21 × (π/180 × 40) = 21 × (π/9) cm.