Cut and General cuboid rule

Duration: 8 min

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  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture covers two main geometry topics: the cut and general cuboid rule, and calculating the longest diagonal of a cuboid. The first section explains that cutting a cube or cuboid into smaller pieces increases the number of pieces and surface area but does not change the total volume. Formulas are provided for calculating the side length of small cubes (a/n), the number of pieces (n^3 or pqr for a cuboid), and the cuts required without stacking (3(n-1) for a cube or (p-1)+(q-1)+(r-1) for a cuboid). The instructor uses visual grids and handwritten annotations to illustrate these concepts. The second section transitions to finding the longest diagonal of a cuboid using the formula d = √(a² + b² + h²). A worked example with dimensions 1.2 cm × 1.3 cm × 1.5 cm is solved, yielding an answer of approximately 2.23 cm from the given options (2.22, 2.32, 2.23, 2.35 cm). The final section briefly introduces a problem on cube surface area to diagonal, where a surface area of 13.5 m² is used with the formula S = 6a² to find a² = 2.25 and a = 1.5 m.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the concept that cutting a cube or cuboid into smaller pieces increases the number of pieces and surface area but does not change total volume. On-screen text displays key formulas: 'Side of each small cube = a/n', 'Number of small cubes = n^3', and 'Cuts required without stacking = 3(n - 1)'. The instructor draws a red grid on the screen to visually represent dividing a cube's faces, writing '1' inside one square. The general cuboid rule is introduced with text showing 'Number of pieces = pqr' and 'Cuts required without rearranging or stacking = (p - 1) + (q - 1) + (r - 1)'. The instructor circles 'a/n' and writes 'a/3' below it, suggesting a specific example where n=3.

  2. 2:00 – 5:00 02:00-05:00

    The lecture continues with the general cuboid rule, emphasizing that cutting does not change total volume. The instructor highlights formulas for side length, number of small cubes, and cuts required, drawing red circles around key terms like 'n', 'n^3', and 'a^3'. The slide then transitions to a new topic: finding the longest diagonal of a cuboid. A problem is presented with dimensions '1.2 cm × 1.3 cm × 1.5 cm' and four options listed (2.22, 2.32, 2.23, 2.35 cm). A wireframe cuboid with a red diagonal arrow is shown at the bottom left. The instructor writes 'd = √' in red handwriting, completing it as 'd = √(a² + b² + h²)' and substituting the values '1.2² + 1.5² + 1.3²'.

  3. 5:00 – 7:34 05:00-07:34

    The instructor completes the longest diagonal calculation, showing 'd = √1.49' with a note and a circled value under the radical sign, arriving at an answer of 2.23 cm from the options. The slide then switches to a new topic titled 'Cube Surface Area to Diagonal', stating the surface area is '13.5 m²'. A red-boxed formula 'S = 6a²' is displayed, with step-by-step work computing 'a² = 13.5/6 = 2.25' and a circled value of '1.5'. This section demonstrates how to find the side length from surface area, which can then be used to calculate the diagonal of a cube.

The lecture progresses from theoretical rules about cutting cuboids to practical applications involving diagonals and surface area. The first part establishes foundational formulas for pieces and cuts, using visual aids like grids to make abstract concepts concrete. The transition to diagonal calculation shows how these geometric principles apply to real problems, with a clear worked example demonstrating the formula d = √(a² + b² + h²). The final section on surface area to diagonal extends the learning by showing how one property (surface area) can be used to find another (side length, and subsequently diagonal). The teaching style combines on-screen text formulas with handwritten annotations, creating a layered explanation that reinforces key concepts through multiple representations. The use of specific numerical examples helps students see how the general rules apply to concrete problems.

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