3D Geometry Important Question

Duration: 3 min

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Module outline

  1. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This short lecture solves a 3D geometry multiple-choice question on the volume of a regular right square pyramid. The problem states that the square base has side length 12 cm and the slant height is 10 cm, asking for the volume with options 384, 480, 576, and 640 cm³. The instructor first identifies the given values a = 12 cm and l = 10 cm, then uses the Pythagorean relation for a regular square pyramid, l² = h² + (a/2)², to find the vertical height. Substituting values gives h² = 100 − 36 = 64, so h = 8 cm. The base area is then calculated as a² = 12² = 144 cm². The volume formula V = (1/3) × base area × height is applied, giving V = (1/3) × 144 × 8. The instructor simplifies by dividing 144 by 3 first to get 48, then multiplies 48 × 8 = 384 cm³. The final answer is 384 cm³, matching option 1.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The slide titled 'Volume of a Regular Square Pyramid' presents the problem: a regular right-pyramid with square base side 12 cm and slant height 10 cm, asking for volume. Red underlines highlight 'a side length' and 'Its slant height is 10 cm,' with red arrows pointing to the pyramid's edges. The instructor writes a = 12cm and l = 10cm, then introduces the relation l² = h² + (a/2)². A small 3D pyramid diagram at lower left shows the slant edge and base side marked with red arrows. The working proceeds to h² = 100 − 36, h² = 64, and a boxed result h = 8.

  2. 2:00 – 2:57 02:00-02:57

    The instructor calculates the base area as 12² = 144 cm² and sets up the volume formula V = (1/3) × B × h with values 144 and 8. A long division of 144 by 3 yields 48, then 48 × 8 = 384 cm³. The final answer 384 cm³ is marked as option 1, the correct choice among options 384, 480, 576, and 640 cm³.

The lesson demonstrates a two-step method for finding the volume of a regular square pyramid when given base side and slant height. Step 1: Use the Pythagorean theorem in the cross-section triangle to find vertical height h from slant height l and half-base a/2, via l² = h² + (a/2)². Step 2: Compute base area a² and apply V = (1/3)a²h. The key teaching cue is simplifying the fraction by dividing base area by 3 before multiplying by height, making arithmetic easier. The worked example yields h = 8 cm and V = 384 cm³.

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