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Three semicircles each of diameter 3 …

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Three semicircles each of diameter 3 cm a circle of diameter 4.5 CM and a semicircle of radius 4.5 CM are drawn in the given figure find the area of shaded region

Posted by Wtsp_Status_Official Goomic 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 11 months ago

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

Answer

Area of semi-circle PQR = ½π(9/2)2

= 81π/8 cm2

Area of region circle, A = π(9/4)2

= 81π/16 cm2

Area of region (B + C) = π(3/2)2

= 9π/4 cm2

Area of region D = ½π(3/2)2

= 9π/8 cm2

Area of shaded region = Area of semicircle - Area of circle - Area of region (B + C) + Area of region D

= 81π/8 - 81π/16 - 9π/4 + 9π/8

= 63π/16 cm2

= 99/8 cm2

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