ব্যাস ও পরিধি (Diameter and Circumference) (১০.৩)

অষ্টম শ্রেণি (মাধ্যমিক ২০২৫) - গণিত বৃত্ত | - | NCTB BOOK
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পাশের চিত্রে, AB এমন একটি জ্যা, যা বৃত্তের কেন্দ্র O দিয়ে গেছে। এরূপ ক্ষেত্রে আমরা বলি, জ্যাটি বৃত্তের একটি ব্যাস। ব্যাসের দৈর্ঘ্যকেও ব্যাস বলা হয়। AB ব্যাসটি দ্বারা সৃষ্ট চাপ দুইটি সমান; এরা প্রত্যেকে একটি অর্ধবৃত্ত। বৃত্তের কেন্দ্রগামী যেকোনো জ্যা, বৃত্তের একটি ব্যাস। ব্যাস বৃত্তের বৃহত্তম জ্যা। বৃত্তের প্রত্যেক ব্যাস বৃত্তকে দুইটি অর্ধবৃত্তে বিভক্ত করে। ব্যাসের অর্ধেক দৈর্ঘ্যকে ব্যাসার্ধ বলে। ব্যাস ব্যাসার্ধের দ্বিগুণ।

বৃত্তের সম্পূর্ণ দৈর্ঘ্যকে পরিধি বলে। অর্থাৎ বৃত্তস্থিত যেকোনো বিন্দু P থেকে বৃত্ত বরাবর ঘুরে পুনরায় P বিন্দু পর্যন্ত পথের দূরত্বই পরিধি। বৃত্ত সরলরেখা নয় বলে রুলারের সাহায্যে বৃত্তের পরিধির দৈর্ঘ্য পরিমাপ করা যায় না। পরিধি মাপার একটি সহজ উপায় আছে। ছবি আকার কাগজে একটি বৃত্ত এঁকে বৃত্ত বরাবর কেটে নাও। পরিধির উপর একটি বিন্দু চিহ্নিত কর। এবার কাগজে একটি রেখাংশ আঁক এবং বৃত্তাকার কার্ডটি কাগজের উপর খাড়াভাবে রাখ যেন পরিধির চিহ্নিত বিন্দুটি রেখাংশের এক প্রান্তের সাথে মিলে যায। এখন কার্ডটি রেখাংশ বরাবর গড়িয়ে নাও যতক্ষণ-না পরিধির চিহ্নিত বিন্দুটি রেখাংশকে পুনরায় স্পর্শ করে। স্পর্শবিন্দুটি চিহ্নিত কর এবং রেখাংশের প্রান্তবিন্দু থেকে এর দৈর্ঘ্য পরিমাপ কর। এই পরিমাপই পরিধির দৈর্ঘ্য। লক্ষ কর, ছোট বৃত্তের ব্যাস ছোট, পরিধিও ছোট; অন্যদিকে বড় বৃত্তের ব্যাস বড়, পরিধিও বড়।

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Request history8.2.28PHP Version102msRequest Duration8MBMemory UsageGET academy/{slug}Route
    • Booting (28.3ms)time
    • Application (73.26ms)time
    • 1 x Application (72.13%)
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      49 templates were rendered
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      uri
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      app/Http/Controllers/Academy/SubjectController.php:102-110
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        • app/Repositories/SubjectRepository.php:94
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        • app/Repositories/SubjectRepository.php:91
        • app/Services/SubjectService.php:32
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        • app/Services/SubjectService.php:43
        • app/Http/Controllers/Academy/SubjectController.php:105
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
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        • app/Repositories/SubjectRepository.php:285
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:122
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:121
        • app/Services/SubjectService.php:60
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        • app/Repositories/SubjectRepository.php:125
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        • app/Repositories/SubjectRepository.php:137
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:136
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        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
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        Backtrace
        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
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        • app/Repositories/SubjectRepository.php:325
        • app/Services/SubjectService.php:76
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        Backtrace
        • app/Repositories/SubjectRepository.php:340
        • app/Services/SubjectService.php:77
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
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        Backtrace
        • app/Services/SubjectService.php:82
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