Question

In figure, find area of shaded region, where OB = 7 cm and OA = 14 cm, and Angle AOC = 40°
(a) 410 cm?
(c) 410.67 cm?
(b) 411 cm
(d) 400 cm
LAROD in which ZB = 90°, if​

Answer 1

Answer:

Step-by-step explanation:

Option (a)

410cm

Answer 2

$From \:the \:figure , Radius (R) = OA = 14 \:cm ,\\radius (r) = OB = 7 \:cm ,\\\angle {AOC} = 40 \degree$

$Area \: of \:the \: shaded \: region \\= (\pi R^{2} - \pi r^{2} ) + Area \: of \: the \:sector\: AOD - Area \:of \:the \:sector \: BOC$

$= (\pi R^{2} - \pi r^{2} ) + \frac{40}{360} \pi R^{2} - \frac{40}{360} \pi r^{2}$

$= \pi (R^{2} - r^{2} ) + \frac{1}{9} \pi (R^{2} - r^{2})$

$= \pi (R^{2} - r^{2} )[ 1 - \frac{1}{9} ]$

$= \frac{22}{7} ( 14^{2} - 7^{2} ) \Big(\frac{8}{9}\Big) \\= \frac{22}{7} \times 147 \times \frac{8}{9} \\= 410.6666\cdot\cdot\cdot \\= 410.67\: cm^{2}$

Therefore.,

$Option \: \pink { ( c ) }\: is \: correct$

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