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Chapter 4 – Mensuration

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

When you look around you, you can find many different objects of various shapes and sizes. And each of these objects may have a different surface area and perimeter. The terms such as perimeter, areas, volumes come under mensuration that is also a chapter in the CBSE class 6th book. Mensuration covers the calculation aspects of the shapes and figures such as the angle, height, surface area, curved surface area, and more. Hence the concept of areas and perimeters are applicable only on the 2D plane figures. Let’s check the various concepts of mensuration in this blog.

It is the boundary length of the given figure. You can consider perimeter as the boundary length that surfaces the given object. Various shapes have different formulas to calculate perimeter. But the best trick to calculate perimeter if you don’t know the formulas is to add all the boundaries individually. You will find the concept of perimeter only in the primary classes as we are more concerned with the complex calculations of the area and volume in higher classes. Since the calculation of perimeter is simple, the calculation and addition of the individual surface dimensions are relatively easy to compute.

The next mensuration concept after the perimeter is the area and volume of solid objects. Hence by a solid object, we mean 3D objects. Volume is always calculated for the 3D objects. We have different types of 3D objects such as spheres, cones, cylinders, and more. The surface area for 3D objects is usually categorised into two parts, namely the total surface area and the lateral/curved surface area. By total surface area, we mean the total body surface of the object, including all the curves and lateral surfaces. The lateral curved surface area means the area associated with the curved/ lateral part of the object. Volume is the space occupied inside the surface area by the elements of the solid.

Cylinders are composed of curved, circular, and straight dimensions with volume. The formula for the surface area of the cylinders is 2*pi*r(r+h), and the volume of the cylinders is pi*r2*h.

Source

You must have seen the cone shape while eating ice-creams. The surface area of the cone is pi* r * (r+l), and the volume of the cone is 1/3* pi*r2*h. Cones are used in the ice-cream cones, funnels, sound amplification, marking cones, and party hats.

Source

A sphere is a solid 3D circular object that has a surface area of 4*pi*r2. The volume of a sphere is 4/3*pi*r3—the different applications of the sphere, the football, golf ball, globe, planets, and more.

There are many applications of mensuration in real-life. Those are listed below.

  • In building walls, the area is used to calculate the number of bricks required for the use.
  • For complex polygons formation, the area, and the perimeter are useful to require the amount of the materials that would be used for construction.
  • Mensuration concept is used widely in the architecture and the construction sector.
  • It is also used in the agriculture sector for the garden pavement tessellation and more.

Mensuration is an important mathematical concept that is a part of geometrical mathematics and comes in the exam. Mensuration forms a major section of the mathematics paper in the exams, along with some of the entrance and competitive exams as well. The basic concept inside the mensuration part is the perimeter, area, and volume. The basic mensuration starts with the concepts of perimeter and areas that are taught in the primary classes. Slowly students are exposed to the major mensuration concepts of the volume of the solid objects. Calculation of the areas and volumes of different shapes and objects requires different formulas and should be learned to tackle any mensuration questions in the examination.

  1. What is mensuration?
    Mensuration is the maths of areas, perimeter, and volumes of objects. They are useful in the construction and architecture industry.
  1. What is the formula of surface area and volume of the cuboid?
    The surface area of the cuboid is 2(l+b+h), and the volume is (l*b*h).
  1. What is the total surface area of the hemisphere?
    The total area of the hemisphere is the sum of the individual areas of the curved and the horizontal part, which leads to 2 π r2 + π r2 = 3 π r2.
  1. What are the two types of areas?
    The two types of areas of solid objects are the total surface area and the curved/ lateral surface area.
  1. What are some of the solid objects for which we can calculate the volume?
    The different 3D objects are parallelogram, rectangle, circle, triangle, cuboid, cube, and hemisphere.
  1. If the radius of the sphere is 3 cm, then find its volume?
    We know that the volume of the sphere is given as 4/3 * pi * r3. Hence the volume will be, 4/3 * 22/7 * 3 * 3 * 3= 113.04 cm3.

At MSVgo video library, you can check the various applications of the mensuration, including the different areas and volumes of the different objects. The concept of cylinder and cone are explained well using the video lessons.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
  • Management Of Natural Resources
  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
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  • Motion in a straight line
  • Moving Charges and Magnetism
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  • Nuclei
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  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
  • Semiconductor Electronics: Materials, Devices and Simple Circuits
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  • Sound
  • Sources Of Energy
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  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
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  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
  • Chemistry of p-Block elements
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  • Study of Compounds
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  • The d-block and f-block elements
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  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
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  • Biological Classification
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  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
  • Environmental Issues
  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
  • Heredity And Evolution
  • Heredity and Variation
  • How Do Organisms Reproduce?
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  • Neural Control And Coordination
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  • Organism and Population
  • Photosynthesis
  • Photosynthesis in Higher Plants
  • Plant Growth and Development
  • Plant Kingdom
  • Pollination and Fertilization
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  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
  • Reproduction in Organisms
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  • Respiration in Human Beings
  • Respiration in Plants
  • Respiratory System
  • Sexual Reproduction in Flowering Plants
  • Strategies for Enhancement in Food Production
  • Structural Organisation in Animals
  • Structural Organisation of the Cell
  • The Endocrine System
  • The Fundamental Unit Of Life
  • The Living World
  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
  • Calculus – Integrals
  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
  • Geometry – Constructions
  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
  • Geometry – Lines and Angles
  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
  • Hydrogen
  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
  • Metals and Non-metals
  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
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