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
ABCD is a field in the shape of a trapezium, AD || BC, ∠ABC = 90° and ∠ADC = 60°. Four sectors are formed with centres A, B, C and D, as shown in the figure. The radius of each sector is 14 m.
Find the following:
(i) total area of the four sectors,
(ii) area of the remaining portion, given that AD = 55 m, BC = 45 m and AB = 30 m.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [Take π = 3.14.]