Radius Affects

Duration: 7 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-2-primary-maths/mensuration-and-geometry/3d-mensuration-solid-figures/asset-radius-affects after enrolling

Inside: a video lesson and guided study material.

Module outline

  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, titled 'Radius Affects,' focuses on the mathematical scaling relationships within cylinder geometry. The instructor begins by establishing that a cylinder's volume is proportional to the square of its radius times its height (r²h), while its curved surface area is proportional to r times h. A central 'Quick results' table demonstrates how specific dimensional changes impact these measurements; for example, doubling the radius quadruples the volume but only doubles the curved surface area. The lesson transitions into a 'Rapid Revision' phase, comparing standard cylinder formulas with those for hollow cylinders and open-ended vessels. Throughout the video, the instructor uses red annotations to circle critical variables like 'rh' and 'r²h', and provides a bilingual (English/Hindi) summary table to reinforce the distinction between radius, diameter, and capacity.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The session opens with the slide 'Radius Affects Cylinder Volume Twice,' introducing the core formulas V = πr²h and curved surface area = 2πrh. The instructor emphasizes that volume is proportional to r²h, while the area is proportional to rh. A 'Quick results' table is presented to show scaling factors, such as how doubling the radius leads to a 4x increase in volume. Red circles are used to highlight these proportional terms, and the instructor writes 'π = 22/7' in red as a practical approximation for calculations.

  2. 2:00 – 5:00 02:00-05:00

    The lecture continues to dissect the 'Quick results' table, specifically circling rows for 'Radius doubled' and 'Height doubled.' The instructor explains that while a radius change affects volume by the square of the factor (k²), it only affects curved area linearly. Specific values like '1.44 times' are boxed in red to illustrate percentage-based changes. The lesson then transitions to a new slide titled 'Cylinder and Hollow Cylinder — Rapid Revision,' where the instructor begins circling formulas for total surface area, 2πr(r + h), and the specific case of a 'One end open' cylinder, 2πrh + πr².

  3. 5:00 – 7:22 05:00-07:22

    In the final segment, the instructor provides a rapid revision of hollow cylinder concepts, highlighting the volume formula nh(R² - r²) and the distinction between outer radius R and inner radius r. A 3D sketch of a cylinder is drawn in the margin to visualize these dimensions. The instructor also notes that 'Cube' or 3D shapes require careful attention to whether the vessel is open or closed. The slide eventually transitions into a Hindi version of the same revision table, ensuring that key terms like 'capacity' and 'internal' dimensions are clearly understood for exam preparation.

The primary pedagogical goal of this lecture is to help students master the non-linear scaling effects in cylinder geometry. By contrasting volume (r²h) with curved surface area (rh), the instructor provides a mental model for quickly solving scaling problems without full recalculation. The use of a 'Quick results' table serves as a high-yield revision tool, allowing students to identify that radius changes have a 'double' impact on volume compared to height. The transition to hollow cylinders and bilingual materials suggests this is part of a broader exam-prep series, likely for competitive mathematics or engineering entrance exams where speed and formula recall are critical. The red annotations act as visual anchors for the most common points of confusion, such as the difference between total surface area and curved surface area.

Loading lesson…