A circular disc of radius 6 cm is divided into three sectors with central angles 90°, 120° and 150°. What part of the whole circle is the sector with central angle150°? Also, calculate the ratio of the areas of the three sectors.
θ1 = 90° θ2 = 120°, θ3 = 150°
Radius of circle = r = 6 cm
Area of circle = πR2
⇒ Area of circle = π×62
⇒ Area of circle = 36π → eqn2
Also, Area of sector (θ3) = 15π cm2
Area of sector (θ2) = 12π cm2→ eqn3
Area of sector (θ1) = 9π cm2→ eqn4
Ratio of three sectors ∷ 9π:12π:15π
Ratio of three sectors ∷ 3:4:5
54