We often see solids like cube, cuboid, prism and pyramid. For three dimensional objects measurements like surface area and volume exist.

**MENSURATION**

*“Nature is an infinite sphere of which the centre is everywhere and*

Pappus, born at Alexandria, Egypt is the last of the great Greek
geometers. Pappus major work ‘Synagoge’ or ‘The Mathematical Collection’ is a
collection of mathematical writings in eight books.

He described the principles of levers, pulleys, wedges, axles and
screws. These concepts are widely applied in Physics and modern Engineering
Science.

·
To
determine the surface area and volume of cylinder, cone, sphere, hemisphere and
frustum.

·
To
compute volume and surface area of combined solids.

·
To
solve problems involving conversion of solids from one shape to another with no
change in volume.

The ancient cultures throughout the world sought the idea of
measurements for satisfying their daily needs. For example, they had to know
how much area of crops needed to be grown in a given region; how much could a
container hold? etc. These questions were very important for making decisions
in agriculture and trade. They needed efficient and
compact way of doing this. It is for this reason, mathematicians thought
of applying geometry to real life situations to attain useful results. This was
the reason for the origin of mensuration. Thus, mensuration can be thought as
applied geometry.

We are already familiar with the areas of plane figures like square,
rectangle, triangle, circle etc. These figures are called 2-dimensional shapes
as they can be drawn in a plane. But most of the objects which we come across
in our daily life cannot be represented in a plane. For example, tubes, water
tanks, bricks, ice-cream cones, football etc. These objects are called solid
shapes or 3-dimensional shapes.

We often see solids like cube, cuboid, prism and pyramid. For
three dimensional objects measurements like surface area and volume exist.

In this chapter, we shall study about the surface area and volume of some of the standard solid shapes such as cylinder, cone, sphere, hemisphere and frustum.

Tags : Mensuration Mensuration

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