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CBSE Class 10 Answered

The boundary of the shaded portion in the given diagram consists of four half circles and two quarter circles. Find the area of the shaded region and length of the boundary, if OA = OB = OC = OD = 14 cm.
Asked by Topperlearning User | 27 Jul, 2017, 01:50: PM
answered-by-expert Expert Answer

O A equals O B equals O C equals O D equals 14 space c m T h e r e f o r e comma space r a d i u s space o f space e a c h space s e m i minus c i r c l e equals 7 space c m rightwards double arrow A r e a space o f space e a c h space s e m i minus c i r c l e equals 1 half πr squared equals 1 half cross times 22 over 7 cross times 7 cross times 7 equals 77 space space c m squared o w comma space r a d i u s space o f space e a c h space q u a d r a n t equals 14 space c m rightwards double arrow A r e a space o f space e a c h space q u a d r a n t equals 1 fourth πr squared equals 1 fourth cross times 22 over 7 cross times 14 cross times 14 equals 154 space c m squared A r e a space o f space s h a d e d space p o r t i o n equals A r e a space o f space t w o space s e m i minus c i r c l e s plus A r e a space o f space t w o space q u a d r a n t s minus A r e a space o f space t w o space s e m i minus c i r c l e s equals left parenthesis 77 space cross times space 2 right parenthesis plus left parenthesis 154 space cross times space 2 right parenthesis space minus left parenthesis 77 space cross times space 2 right parenthesis space c m squared equals 308 space c m squared space space C i r c u m f e r e n c e space o f space e a c h space s e m i minus c i r c l e equals 1 half cross times 2 πr equals 1 half cross times 2 cross times 22 over 7 cross times 7 equals 22 space c m A n d comma space C i r c u m f e r e n c e space o f space e a c h space q u a d r a n t equals 1 fourth cross times space 2 straight pi r equals 1 fourth cross times 2 cross times 22 over 7 cross times 14 equals 22 space c m rightwards double arrow L e n g t h space o f space t h e space b o u n d a r y equals left parenthesis 22 space cross times space 4 right parenthesis space plus space left parenthesis 2 space cross times space 22 right parenthesis equals 88 plus 44 equals 132 space c m

Answered by | 27 Jul, 2017, 03:50: PM

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