In this lesson you’ll learn about the basics, concepts and important properties
related to the Surface area and Volume of solids. The presentation covering such
content will be done by the instructor in own handwriting, using video and with
the help of several examples with solution. This will help you understand
important geometry properties and relationships to solve problems from day
to day life situations based on the above concepts, and how to make use of
them.
As stated above, such objects which occupy space
(i.e., they have three dimensions) are called solids.
To have deeper understanding look at the example of brick: (Fig: 1)
A brick has six surfaces and eight vertices. The sum of the areas of all the six surfaces is called the Surface Area of the brick. Then it occupies the space, and it is called volume of thee brick. Thus it can be stated:
every 3D object occupies a finite volume depending on the dimensions. The measure of part of space occupied by a solid is called its Volume.
(Continued from above)
Now, you’ll learn important properties and relationships of some solids like:
a cuboid, cylinder, cone and a sphere and learn to find their surface areas and
volumes. You may recall the meaning of polyhedron to begin with to go for deeper
understanding. In geometry, a polyhedron is simply a three-dimensional solid
which consists of a collection of polygons, usually joined at their edges.
In brief, the important properties of common solids are as below:
Refer Fig: 2, above: Cube: A Cuboid; where its length, breadth and height are equal i.e. where all side lengths equal and all angles measure 90,
is known as ‘Cube’.
Prism: The cross-section remains same throughout, see prism triangular in shape.
Cylinder: It has circular base.
Pyramid: The slant edges are of equal length in a right pyramid (the pyramid with square base).
The measurement for Area is expressed in square units such as- cm2,
m2, in2, etc.
The volume of a three-dimensional figure can be said to be a measure of the number
of cubic units needed to fill the space inside an object. It is measured in cubic
units such as cm3, m3, in3, etc.
E.g. surface area and volume of a rectangular
box of length length l, width w, and height h, is given by:
Surface area =
2(lw
+ wh + hl)
Volume = l w h
The video above will explain more in detail about applying concepts of Surface
area and Volume of solids, with the help of several examples and done watching video. This helps you to deal with solving problems related to surface area and volume of solids and help doing the Geometry home work.
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is known as ‘Cube’.