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.

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