Question

For the sectors with given measures, find the length of the arc, area and perimeter, (π = 3.14)

(i) central angle 45°, r = 16 cm

(ii) central angle 120°, d = 12.6 cm

(iii) central angle 60°, r = 36 cm

(iv) central angle 72°, d = 10 cm

Answer 1

(i) Central angle 45°, r = 16 cm

Length of the arc l = θ°/360° × 2πr units

l = 45°/360° × 2 × 3.14 × 16 cm

l = 1/8 × 2 × 3.14 × 16 cm

l = 12.56 cm

Area of the sector = θ°/360° × πr²

A = 45°/360° × 3.14 × 16 × 16

A = 100.48 cm²

Perimeter of the sector

P = l + 2r units

P = 12.56 + 2(16) cm

P = 44.56 cm

(ii) Central angle 120°, d = 12.6 cm

∴ r = 12.62 cm

r = 6.3 cm

Length of the arc

Area of the sector missing

Perimeter of the sector

P = l + 2r units

P = 6.28 + 2(5) cm

P = 6.28 + 10 cm

P = 16.28 cm