Question

In the given figure two concentric circle with Centre O have radii 21 cm and 42 CM if angle AOB is equal to 60 degree find the area of the shaded region is (use
\pi
is equal to 22/7)

Answer 1

Radii of the concentric circles = 21 cm and 42 cmArea between the circles = π R2 - r2 = (22/7) (422 - 212) = 4158 cm2Angle subtended by the arc in the inner circle = 60°
Area of the sector in the inner circle = (60° / 360°) x π r2 = (60° / 360°) x (22/7) x (21)2 = 231 cm2Angle subtended by the arc in the outer circle = 60°
Area of the sector in the inner circle = (60° / 360°) x π R2 = (60° / 360°) x (22/7) x (42)2 = 924 cm2Area of the portion of the sector in between the circles = 924 - 231 = 693 cm2
Area of the shaded portion = (Area between the circles) - (Area of the portion of the sector in between the circles)
 = 4158 - 693= 3465Therefore, the area of the shaded region is 3465 cm2.