SSC (Marathi Semi-English) 10thMaharashtra State Board
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In the Given Figure, Square Abcd is Inscribed in the Sector a - Pcq. the Radius of Sector C - Bxd is 20 Cm. Complete the Following Activity to Find the Area of Shaded Region - SSC (Marathi Semi-English) 10th - Geometry

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Question

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region 

Solution

Side of square ABCD = radius of sector C-BXD = 20 cm Area of square = (side)2 = 20= 400 cm

Area of shaded region inside the square 
= Area of square ABCD − Area of sector C-BXD
= 400  \[- \frac{\theta}{360° } \times \pi r^2\]

= 400  \[- \frac{90° }{360° } \times \frac{3 . 14}{1} \times \frac{400}{1}\]

= 400 - 314 

= 86 cm2

Radius of bigger sector = Length of diagonal of square ABCD  = \[20\sqrt{2}\] cm 

Area of the shaded regions outside the square 
= Area of sector A-PCQ − Area of square ABCD
= A(A-PCQ) − A( ABCD ) =  \[\frac{\theta}{360° } \times \pi \times r^2\] - 202  =

\[\frac{90°}{360°} \times 3 . 14 \times \left( 20\sqrt{2} \right)^2\] - (20)= 628 - 400 = 228 cm

  ∴ Total surface area of the shaded region = 86 + 228 = 314 cm2

 
 
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Solution In the Given Figure, Square Abcd is Inscribed in the Sector a - Pcq. the Radius of Sector C - Bxd is 20 Cm. Complete the Following Activity to Find the Area of Shaded Region Concept: Surface Area of a Combination of Solids.
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