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(B) The shaded region is the area between two sectors of circles with the same central angle $	heta = 90^\circ$.Let $R$ be the radius of the outer se

Vedclass · Accepted Answer

$192.5$

Vedclass · Answer

(B) The shaded region is the area between two sectors of circles with the same central angle $	heta = 90^\circ$.Let $R$ be the radius of the outer sector $(OB = 21 \, 	ext{m})$ and $r$ be the radius of the inner sector $(OD = 14 \, 	ext{m})$.The area of a sector is given by $\frac{	heta}{360^\circ} 	imes \pi R^2$.The area of the shaded region = (Area of outer sector) - (Area of inner sector)$= \frac{90^\circ}{360^\circ} 	imes \pi 	imes R^2 - \frac{90^\circ}{360^\circ} 	imes \pi 	imes r^2$$= \frac{1}{4} 	imes \pi 	imes (R^2 - r^2)$$= \frac{1}{4} 	imes \frac{22}{7} 	imes (21^2 - 14^2)$$= \frac{1}{4} 	imes \frac{22}{7} 	imes (441 - 196)$$= \frac{1}{4} 	imes \frac{22}{7} 	imes 245$$= \frac{1}{4} 	imes 22 	imes 35$$= \frac{770}{4} = 192.5 \, 	ext{m}^2$.

In the given diagram,the shaded portion represents a flower bed in a plot. If $m \angle O = 90^\circ$,$OB = 21 \, \text{m}$,and $OD = 14 \, \text{m}$,find the area of the flower bed in $\text{m}^2$.

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