Visualising 3D Shapes Video Lecture - Class 8

visualizing 3d shapes
in this module you will learn about
visualizing 3d shapes we live in a
three-dimensional world every object we
see or touch has three dimensions that
can be measured by length width and
height for example a television has
three dimensions that can be measured by
length width and height and so on every
object that we see has different views
and this view depends on the direction
from which we are looking at the object
the different types of views our top
view side view and front view
now let us see the different views of a
dice top view of a dice side view of a
dice front view of a dice
similarly here is different views of a
car top view side view front view
observe the solid shapes which are
formed by arranging some units of cubes
it looks different from different
position but the object is same first
let us see different views of solids
made of three cubes its top view side
view and front view now let's see solid
shape made of four cubes let us see the
front view side view and top view of
some more objects we use map since we
were in primary class we use maps to
find a particular location reverse
mountain etc here is a map drawn by
Simmi in this map the route from her
house to a friend's house is shown can
you find out how far is semies house
from a friend's house it is very
difficult to answer the above questions
on the basis of the given math as we do
not know if the distances between the
circles there is no proper information
in this map now let's have a look at
this map drawn by her brother Sahil
Sahil uses different symbols for
Landmarks longer lines have been drawn
for longer distance and short lines have
been used for shorter distance he has
drawn a map with a scale symbols and
distances will help us to read the map
easily the actual distance is denoted by
one centimeter or one millimeter in the
map this means if one draws a mat he or
she has to decide that one centimeter
space in the mat shows certain distance
say one kilometer or ten kilometers the
scale will vary from map to mat and not
within the map let us learn about
polyhedron each of the solids is made up
of polygonal regions which are called
its faces these faces meet at edges
which are line segments and the edges
meet at word Isis which are points such
solids are called polyhedrons a
polyhedron is a solid with flat faces
and curved or lateral surfaces are non
polyhedron cubes cuboids prisms are a
few examples of polyhedrons
spheres cones and cylinders are a few
examples of non polyhedrons the faces of
cubes are squares the faces of
rectangular prism are rectangles hence
these solids are polyhedron the surface
of sphere is curved the surface of cone
and cylinder is lateral as they are
called non polyhedron polyhedron can be
classified into convex and non convex
polyhedron and regular and non-regular
polyhedron first let's learn about
convex and non convex polyhedron if the
line segment joining any two points on
the surface of the polyhedron lies on
the surface and does not intersect
itself it is called convex polyhedron
the idea of convex polyhedron is similar
to
mcc's polygons and if the line segment
joining any two points on the surface of
the polyhedron does not lie on the
surface then it is called as non convex
polyhedron now let us see regular
polyhedron x' and non regular polyhedron
the polyhedron whose faces are made up
of regular polygons and are congruent
and the same number of faces meet at
each vertex is said to be regular
polyhedron
for example cube is a regular polyhedron
its faces are congruent regular polygons
vertices are formed by the same number
of faces more examples of convex
polyhedron are tetrahedron octahedron
dodecahedron and icosahedron are regular
polyhedron now look at this square
pyramid this polyhedron is not regular
all the sides are congruent but its
vertices are not formed by the same
number of faces one vertex is formed by
four edges and other vertices are formed
by three edges a prism is a polyhedron
in which two faces are parallel and
congruent polygons called
its basis and whose other faces are
parallelograms call its lateral faces
there are many types of prisms the type
of prism is determined by the shape of
the base for example a triangular prism
will have triangular bases while a
square prism will have square bases a
hexagonal prism will have hexagonal
bases and so on on the other hand a
pyramid is a polyhedron for which one
face called the base is a polygon and
all other faces called lateral faces are
triangles if the base is called the
bottom of the pyramid the top point is
called its apex
as with prisms there are many types of
pyramids often classified by the shapes
of their bases for example a triangular
pyramid will have triangular basis while
a square pyramid will have square basis
a pentagonal pyramid will have Pentagon
bases and so on have you ever heard
about Euler's formula for many solid
shapes the number of faces plus the
number of vertices minus the number of
edges always equals 2 this can be
written as f plus V minus E is equal to
2
in fact this formula is true for any
polyhedron no matter what we do we
always end up with 2 let's try it on the
cuboid a cuboid has 6 faces 8 vertices
and 12 edges so 6 plus 8 minus 12 is
equal to 2 now let's tabulate the number
of faces edges and vertices for the
following polyhedron here F stands for
number of faces V stands for number of
vertices and E stands for number of
edges from the last two columns we find
that F plus V is equal to e plus 2
therefore F plus V minus E is equal to 2
as we know this relation is called
Euler's formula let us revise all that
we learned in this module on visualizing
3d shapes
you