In the diagram the area swept by the wiper of a car is shown, the area of the shaded portion is $102.7 C m^{2}$
If true then enter $1$ and if false then enter $0$

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Solution

$S i n c e O B & O C a r e t h e s a m e w i p e r, O B = O C = O A + A B = (7 + 14) c m = 21 c m . ∴ O B C i s a s e c t o r w i t h O C o r O B a s r a d i u s = r_{1} = 21 c m & ∠ O = θ^{o} = 30^{o} & O A D i s a s e c t o r w i t h O A o r O D a s r a d i u s = r_{2} = 7 c m & ∠ O = θ^{o} = 30^{o} . ∴ a r s h a d e d p o r t i o n (A B C D) = a r s e c t o r O B C - a r s e c t o r O A D . = \frac{θ^{o}}{360^{o}} \times π \times {r_{1}}^{2} - \frac{θ^{o}}{360^{o}} \times π \times {r_{2}}^{2} = \frac{θ^{o}}{360^{o}} \times π \times ({r_{1}}^{2} - {r_{2}}^{2}) = \frac{30^{o}}{360^{o}} \times \frac{22}{7} \times (21^{2} - 7^{2}) {c m}^{2} = 102.7 {c m}^{2} . A n s - a r s h a d e d p o r t i o n (A B C D) = 102.7 {c m}^{2} .$

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