AB and CD are respectively arcs of two concentric circles of diameters 14cm and 21cm respectively and centre O. If AOB = 30 degree, find the area of the shaded portion ( please give me a correct answer that actually makes sense )
Answers
Answer:
16.04 cm²
here is your answer buddy
Given : AB and CD are respectively arcs of two concentric circles of diameters 14cm and 21cm respectively and centre O.
AOB = 30 degree,
To find : the area of the shaded portion
Solution:
Area of the shaded portion = area of sector AOB - area of sector COD
area of sector of circle = ( sector angle / 360° ) π (radius)²
sector angle = 30°
Radius = Diameter/2
Diameter 21 cm => radius = 21/2 cm
Diameter = 14 cm => radius = 14/2 = 7 cm
area of sector AOB = ( 30/360) π (21/2)²
= (1/12) (22/7) (21)² / 4
= 22 * 21 / 16
= 11 * 21 / 8
= 28.875
area of sector COD = ( 30/360) π (7)²
= (1/12) (22/7) (7)²
= 11 * 7 / 6
= 77/6
= 12.8333
Area of the shaded portion = 28.875 - 12.8333
= 16.0417
area of the shaded portion = 16.0417 cm²
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