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In Figure 2, two concentric circles with centre O, have radii 21 cm and42 cm. If AOB 60°, find the area of the shaded region.60°Figure 2 |
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Answer» Sol:Radii of the concentric circles = 21 cm and 42 cm Area between the circles = π R2- r2= (22/7) (422- 212) = 4158 cm2 Angle 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 cm2 Angle 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 cm2 Area of the portion of the sector in between the circles = 924 - 231 = 693 cm2Area 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. |
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