# In Figure 2, Two Concentric Circles with Centre O, Have Radii 21 Cm and 42 Cm. If ∠Aob = 60°, Find the Area of the Shaded Region. - Mathematics

Sum

In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.

#### Solution

Radius of inner circle, OC = 21 cm

Radius of outer circle, OA = 42 cm

Area of a circle with radius R = piR^2 = pi(42)^2

Area of a circle with radius r = pir^2 = pi(21)^2

Area of sector AOB = theta/360 xx piR^2 = 60/360 xx pi(42)^2 = (pi(42)^2)/6

Area of sector COD = theta/360 xx pir^2 = 60/360 xx pi(21)^2 = (pi(21)^2)/6

Area of shaded portion = Area of circle with radius R - Area of circle with radius r - [Area of sector AOB - Area of sector COD]

= pi(42)^2 - pi(21)^2 - [(pi(42)^2)/6 - (pi(21)^2)/6]

= pi[(42)^2 - (21)^2 - 1/6[(42)^2 - (21)^2]]

= pi[((42)^2 - (21)^2)(1 - 1/6)]

= pi[(42 - 21)(42 + 21)5/6]

= 22/7 xx 5/6 xx 21 xx 63

= 3465 cm2

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