Cube and Special Cuboid
Duration: 8 min
This video lesson is available to enrolled students.
Inside: a video lesson and guided study material.
Module outline
- हिंदी / Hindi — भाषा खंड: अपठित गद्यांश और अपठित पद्यांश, वर्ण-विचार (भाषा, लिपि और वर्णमाला), वर्तनी और वर्ण-विन्यास, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, वाक्य-शुद्धि, अशुद्धि शोधन और विराम चिह्न, उपसर्ग और प्रत्यय, संधि, समास, तत्सम, तद्भव, देशज और विदेशी शब्द, शब्द-भंडार, मुहावरे और लोकोक्तियाँ, अलंकार, रस और छंद, मिश्रित अभ्यास (बहु-विषयक सामग्री), शब्दोत्पत्ति एवं भाषा-बोलियाँ, वाक्य-पूर्ति, अनुच्छेद-रचना
- संस्कृत / Sanskrit — भाषा खंड: वर्ण, उच्चारण, सन्धि, शब्दरूप, धातुरूप, कारक-विभक्ति, समास, प्रत्यय, उपसर्ग, वाच्य, सङ्ख्या, अव्यय, अपठित अवबोधन
- अंग्रेज़ी / English — भाषा खंड: Noun, Pronoun, Determiner, Articles, Adjectives, Verb, Adverb, Preposition, Conjunction, Interjection, Sentence Structure, Phrases & Clauses, Tenses, Subject Verb Agreement (Verb Noun Agreement), Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Vocabulary, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage)
- सामान्य ज्ञान एवं समसामयिक घटनाएँ / General Knowledge & Current Affairs — 25 प्रश्न: Static GK — Books & Authors, Awards, Sports, Important Days, Firsts, Organisations, Culture & Arts, Current Affairs — National, Current Affairs — International, Economy & Government Schemes (current), Uttar Pradesh, History, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs
- गणित / Mathematics — 16 प्रश्न: Number System & Place Value, Whole Numbers & Four Operations, Factors, Multiples, Divisibility, HCF & LCM, Fractions & Decimals, Integers & Rational Numbers, Exponents, Powers, Squares, Cubes & Roots, Algebra — Expressions, Identities & Linear Equations, Ratio, Proportion & Percentage, Measurement — Length, Mass, Capacity, Time, Money, Commercial Arithmetic (Profit-Loss-Discount, SI & CI), Average, Ages & Mixtures, Time & Work, Speed-Time-Distance, Geometry — Shapes, Lines & Angles, Symmetry, Spatial Understanding, Geometry — Triangles, Quadrilaterals, Circles, Congruence & Constructions, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Higher Mathematics — Trigonometry, Quadratics, Polynomials, Progressions, Statistics, Logarithms, Number System, Arithmetic, Divisibility Rules, HCF LCM, Powers and Exponents (Surds and Indices), Algebra, Ratio and Proportion (Ratios), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Mensuration and Geometry, Statistics
- विज्ञान / Science — 8 प्रश्न: Food, Nutrition & Components of Food, Plants — Nutrition, Transport, Reproduction, Animals & Human Body — Systems, Organs, Nutrition, Health, Diseases, Microorganisms & Hygiene, Cell, Tissues & Classification of Living Beings, Reproduction & Adolescence, Physical Quantities, Units & Measurement, Materials, Matter, Mixtures & Separation, Atoms, Molecules & Structure of Matter, Elements, Compounds, Acids-Bases-Salts, Metals & Non-metals, Physical & Chemical Changes, Combustion, Fuels, Carbon & Organic Compounds, Motion, Force, Pressure & Friction, Heat & Temperature, Light, Shadows, Mirrors & Lenses, Work, Energy & Power, Sound, Electricity & Magnetism, Earth, Universe & Solar System, Natural Resources, Environment, Ecosystem & Pollution, Science & Technology in Daily Life (inventions, space, defence), Biology, Chemistry, Physics
- पर्यावरण एवं सामाजिक अध्ययन / Environment & Social Studies — 8 प्रश्न: Environment Conservation, Waste & Pollution, Natural Disasters & Safety, Water (sources, conservation), Air, Weather, Sky & Seasons, Travel, Transport & Communication, Festivals, Culture & Heritage (India), Food & Nutrition, Health & Hygiene, Plants (types, parts, uses), Animals (habitats, features, care), History — Sources, Prehistory & Harappan Civilisation, History — Vedic Age, Mahajanapadas, Religions (Buddhism/Jainism), History — Mauryas, Guptas & Post-Gupta Kingdoms, History — Medieval India (Sultanate, Mughals, Regional Kingdoms, Bhakti-Sufi), History — Modern India & Colonial Rule, History — Indian National Movement (1857–1947), History — India Since Independence, Geography — Earth, Globe, Maps, Latitudes-Longitudes, Geography — Landforms, Atmosphere, Hydrosphere, Climate, Natural Vegetation & Biomes, Geography — Physical & Political India (rivers, mountains, soils, vegetation, climate), Geography — Resources, Agriculture, Industries, Transport, Geography — World (continents, countries, oceans), Geography — Population, Settlements & Census, Polity — Democracy, Diversity, Social Justice & Gender, Polity — Constitution, Preamble, Fundamental Rights & Duties, DPSP, Polity — Union & State Government, Parliament, Judiciary, Elections, Polity — Local Government (Panchayati Raj, Urban bodies), Polity — International Relations & Organisations, Economy — Basic Concepts, Money, Banking, Budget, Schemes, Economy — Consumer Rights & Protection, Geography, Environment
- शिक्षण कौशल / Teaching Skills — 8 प्रश्न: Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Classroom Management & Communication, Teaching-Learning Aids & ICT Integration, Curriculum & School Environment, Lesson Planning, Micro-Teaching & Teaching Skills, Evaluation, Assessment & Measurement, Inclusive Education & Special Needs, Policies, Acts & Contemporary Issues
- बाल मनोविज्ञान / Child Psychology — 8 प्रश्न: Concept of Pedagogy, Psychology, Child Development, Theories, Personality Development, Individual Differences, Learning and Motivation, Understanding Diverse Learners, Inclusive Education, Teaching-Learning Process, Teaching Methods & Strategies, Experiential Pedagogy, Assessment & Evaluation, National Education Policy (NEP) 2020, Curriculum Framework & Reforms, Miscellaneous Topics
- जीवन कौशल, प्रबन्धन एवं अभिवृत्ति / Life Skills, Management & Attitude — 8 प्रश्न: Professional Development & Ethics, Guidance, Counselling & Mental Health, Mental Health & Life Skills
- तार्किक ज्ञान / Logical Reasoning — 5 प्रश्न: Number/Alphabet Test, Mathematical Operations, Cubes & Dices, Inequality, Selection Decision Table (Decision Making), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Western Logic, 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, Venn Diagram, Syllogism, Analogy, Ranking, Order and Sequence, Mirror & Water Image, Embedded/Figure Completion, Paper Folding & Cutting, Data Interpretation
- सूचना तकनीकी / Information Technology — 4 प्रश्न: Terms & Abbreviations, MS Office Applications, Keyboard Shortcuts, Emerging Tech Trends, Digital India & e-Gov
- अतिरिक्त अभ्यास (वैकल्पिक) / Extra Practice — beyond the 2026 syllabus: हिंदी साहित्य — कवि, लेखक, रचनाएँ, संस्कृत साहित्य-कवि-ग्रन्थ, History — World History (basic)
AI summary & chapters
AI Summary
An AI-generated summary of this video lecture.
This lecture explains that a cube is a special case of a cuboid where all three dimensions are equal. It compares the formulas for lateral surface area, total surface area, and volume of a general cuboid (length l, breadth b, height h) with those of a cube (side a). The lesson then distinguishes between face diagonals and space diagonals, deriving the space diagonal formula d = √(l² + b² + h²) using the Pythagorean theorem. Finally, it shows how one cube measurement can reveal all others: side a = √(S/6) from total surface area S, and a = ³√V from volume V.
Chapters
0:00 – 2:00 00:00-02:00
The video introduces the title 'A Cube Is a Special Cuboid' and defines cuboid dimensions as Length = l, Breadth = b, Height = h. It establishes that a cube has all three dimensions equal (l = b = h = a). A comparison table is presented to differentiate the lateral surface area, total surface area, and volume formulas for both shapes. The instructor uses red annotations to circle the cube diagram and underline key terms like 'Lateral surface area' and 'Volume', highlighting formulas such as 2h(l + b) vs 4a² for lateral surface area and lbh vs a³ for volume.
2:00 – 5:00 02:00-05:00
The lecture continues with the comparison table, adding a note '2 (l b h)' and circling the volume term 'lbh'. The left panel lists 'Common structural facts' including Faces = 6, Edges = 12, and Vertices = 8. The focus then shifts to distinguishing between face diagonals and space diagonals. The instructor highlights the formula for the face diagonal on the l x b face as √(l² + b²) and for a cube of side a as a√2. A step-by-step derivation is provided to explain why the space diagonal formula d = √(l² + b² + h²) works, utilizing the Pythagorean theorem twice. A red line representing the space diagonal is drawn on the 3D cuboid model.
5:00 – 7:59 05:00-07:59
The video presents a summary slide titled 'One Cube Measurement Can Reveal All the Others'. It details the mathematical relationships between the side length, total surface area (S = 6a²), volume (V = a³), and space diagonal (d = a√3) of a cube. The instructor highlights key formulas in red ink to show how one measurement can be used to derive the others, specifically writing a = √(S/6) and a = ³√V. The final frame shows the same content translated into Hindi, providing a multilingual summary for better understanding.
The lecture builds from the basic definition of a cube as a special cuboid to more complex geometric properties. It starts by establishing the dimensional equality (l = b = h = a) and uses this to compare surface area and volume formulas. The progression then moves to diagonal lengths, clearly distinguishing between face diagonals (which lie on a single plane) and space diagonals (which pass through the interior). The derivation of the space diagonal formula using the Pythagorean theorem twice is a key methodological point. The lesson concludes by showing the interdependence of cube measurements, allowing students to calculate any property if they know just one value. The use of red annotations and a final Hindi summary reinforces the core formulas for exam revision.