ঘনবস্তু (Solid) (৮.৫)

অষ্টম শ্রেণি (মাধ্যমিক ২০২৫) - গণিত চতুৰ্ভুজ | - | NCTB BOOK
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বই, বাক্স, ইট, ফুটবল ইত্যাদি ঘনবস্তু। ঘনবস্তু আয়তাকার, বর্গাকার, গোলাকার ও অন্যান্য আকারের হতে পারে। ঘনবস্তুর দৈর্ঘ্য, প্রস্থ ও উচ্চতা আছে।

চিত্র-১ এর বস্তুটি আয়তাকার ঘনবস্তু। এর মোট ছয়টি আয়তাকার পৃষ্ঠ বা তল আছে যাদের প্রত্যেকটি একটি আয়তক্ষেত্র। পরস্পর বিপরীত পাশের পৃষ্ঠদ্বয় সমান ও সমান্তরাল। কাজেই পরস্পর বিপরীত পাশের দুইটি পৃষ্ঠের ক্ষেত্রফল সমান। চিত্র-২ এর বস্তুটি বর্গাকার ঘনবস্তু। এর মোট ছয়টি পরস্পর সমান বর্গাকার পৃষ্ঠ বা তল আছে যাদের প্রত্যেকটি একটি বর্গক্ষেত্র। আবার, পরস্পর বিপরীত পৃষ্ঠদ্বয় সমান্তরাল। বর্গাকার ঘনবস্তুকে ঘনক (cube) বলা হয়। পরস্পর দুইটি করে পৃষ্ঠের ছেদ-রেখাংশকে ঘনকের ধার বা বাহু বলা হয়। ঘনকের সকল ধার বা বাহু পরস্পর সমান। কাজেই ঘনকের সকল পৃষ্ঠের ক্ষেত্রফল পরস্পর সমান।

 

ঘনবস্তুর পৃষ্ঠের ক্ষেত্রফল নির্ণয় :

(ক) আয়তাকার ঘনবস্তু : একটি আয়তাকার ঘনবস্তুর দৈর্ঘ্য a একক হলে, চিত্রানুসারে, ঘনবস্তুটির সমগ্র পৃষ্ঠের ক্ষেত্রফল = {(ab ab) + (bc + bc) + (ac + + ac)} বর্গএকক = 2(ab + bc + ac) বর্গ একক (খ) ঘনক : একটি ঘনকের ধার a একক হলে, এর ছয়টি পৃষ্ঠের প্রতিটির ক্ষেত্রফল = a x a বর্গ একক = a2 বর্গ একক । অতএব, ঘনকটির সমগ্র পৃষ্ঠের ক্ষেত্রফল = 6a2 বর্গ একক।

উদাহরণ। একটি আয়তাকার ঘনবস্তুর দৈর্ঘ্য 7.5 সে.মি., প্রস্থ 6 সে.মি ও উচ্চতা 4 সে.মি.। ঘনবস্তুটির সমগ্র পৃষ্ঠের ক্ষেত্রফল নির্ণয় কর।

সমাধান : আমরা জানি, কোনো আয়তাকার ঘনবস্তুর দৈর্ঘ্য a একক, প্রস্থ b একক ও উচ্চতা c একক হলে, বস্তুটির সমগ্র পৃষ্ঠের ক্ষেত্রফল 

=2(ab +bc +ac) বর্গ একক।

এখানে, a = 7.5 সে.মি., b = 6 সে.মি. এবং c = 4 সে.মি.

∴ প্রদত্ত আয়তাকার ঘনবস্তুটির সমগ্র পৃষ্ঠের ক্ষেত্রফল

= 2 (7.5 × 6 + 6 × 4 + 7.5 × 4) বর্গ সে.মি.

= 2(45 + 24 + 30) বর্গ সে.মি.

= 2 × 99 বর্গ সে.মি.

= 198 বর্গ সে.মি.

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Request history8.2.28PHP Version86.22msRequest Duration7MBMemory UsageGET academy/{slug}Route
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      app/Http/Controllers/Academy/SubjectController.php:102-110
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        • app/Repositories/SubjectRepository.php:285
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        • app/Repositories/SubjectRepository.php:285
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        • app/Repositories/SubjectRepository.php:285
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        • app/Repositories/SubjectRepository.php:140
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        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      App\Models\Subject
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      App\Models\PackagePlan
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      App\Models\SubjectDescription
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      App\Models\User
      2User.php#?
      App\Models\SubCategory
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          Date ↕MethodURLData
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