PROJECTION OF SOLID
A solid has three dimensions, viz. length, breadth and thickness. To represent a solid on a
flat surface having only length and breadth, at least two orthographic views are
necessary. Sometimes, additional views projected on auxiliary planes become necessary
to make the description of a solid complete.
Solids may be divided into two main groups:
(1) Polyhedron
(2) Solids of revolution
1. Polyhedron : A polyhedron is defined as a solid bounded by planes called faces.
When all faces are equal and regular, the polyhedron is said to be regular.
Ex- Tetrahedron , Cube , Octahedron, Prism, Pyramid
Tetrahedron : It has four equal faces, each an equilateral triangle.
Cube : It has six faces, all equal squares.
Octahedron: It has eight equal equilateral triangles as faces.
Prism: This is a polyhedron having two equal and similar faces called its ends or bases,
parallel to each other and joined by other faces which are parallelograms. The imaginary
line joining the centres of the bases is called the axis.
A right and regular prism has its axis perpendicular to the bases. All its faces are equal
rectangles.
PROJECTION OF SOLID
PROJECTION OF SOLID
Pyramid: This is a polyhedron having a plane figure as a base and a number of triangular faces
meeting at a point called the vertex or apex. The imaginary line joining the apex with the
centre of the base is its axis.
A right and regular pyramid has its axis perpendicular to the base which is a regular plane
figure. Its faces are all equal isosceles triangles.
Oblique prisms and pyramids have their axes inclined to their bases.
Prisms and pyramids are named according to the shape of their bases, as triangular, square,
pentagonal, hexagonal etc.
PROJECTION OF SOLID
2. Solids of revolution:
Cylinder : A right circular cylinder is a solid generated by the revolution of a rectangle about
one of its sides which remains fixed. It has two equal circular bases. The line joining the
centres of the bases is the axis. It is perpendicular to the bases.
Cone : A right circular cone is a solid generated by the revolution of a right-angled triangle
about one of its perpendicular sides which is fixed.
Sphere : A sphere is a solid generated by the revolution of a semi-circle about its diameter as
the axis.
PROJECTION OF SOLID
Frustum: When a pyramid or a cone is cut by a plane parallel to its base, thus removing
the top portion, the remaining portion is called its frustum
Truncated: When a solid is cut by a plane inclined to the base it is said
to be truncated.
PROJECTION OF SOLID IN SIMPLE POSITION
A solid in simple position may have its axis perpendicular to one reference plane or parallel
to both. When the axis is perpendicular to one reference plane, it is parallel to the other.
Also, when the axis of a solid is perpendicular to a plane, its base will be parallel to that
plane. We have already seen that when a plane is parallel to a reference plane, its projection
on that plane shows its true shape and size.
Therefore, the projection of a solid on the plane to which its axis is perpendicular,
will show the true shape and size of its base.
Hence, when the axis is perpendicular to the ground, i.e. to the H.P., the top view
should be drawn first and the front view projected from it.
When the axis is perpendicular to the V.P., beginning should be made with the
front view. The top view should then be projected from it.
When the axis is parallel to both the H.P. and the V.P., neither the top view nor
the front view will show the actual shape of the base. In this case, the projection
of the solid on an auxiliary plane perpendicular to both the planes, viz. the side view
must be drawn first. The front view and the top view are then projected from the
side view. The projections in such cases may also be drawn in two stages.
PROJECTION OF SOLID
Axis perpendicular to the H.P.:
Problem 1 : Draw the projections of a triangular prism, base 40 mm side and axis 50 mm
long, resting on one of its bases on the H.P. with a vertical face perpendicular to the V.P.
PROJECTION OF SOLID
Problem 1 : Draw the projections of a triangular prism, base 40 mm side and axis 50 mm
long, resting on one of its bases on the H.P. with a vertical face perpendicular to the V.P.
PROJECTION OF SOLID
Problem 2 : Draw the projections of a pentagonal pyramid, base 30 mm edge and axis 50
mm long, having its base on the H.P. and an edge of the base parallel to the V.P. Also
draw its side view.
PROJECTION OF SOLID
Problem 2 : Draw the projections of a pentagonal pyramid, base 30 mm edge and axis 50
mm long, having its base on the H.P. and an edge of the base parallel to the V.P. Also
draw its side view.
PROJECTION OF SOLID
Problem 3 : Draw the projections of (i) a cylinder, base 40 mm diameter and axis 50 mm
Jong, and (ii) a cone, base 40 mm diameter and axis 50 mm long, resting on the H.P. on
their respective bases.
PROJECTION OF SOLID
Problem 3 : Draw the projections of (i) a cylinder, base 40 mm diameter and axis 50 mm
Jong, and (ii) a cone, base 40 mm diameter and axis 50 mm long, resting on the H.P. on
their respective bases.
PROJECTION OF SOLID
Problem 4 : Draw the projections of a hexagonal pyramid, base 30 mm side and axis 60
mm long, having its base on the H.P. and one of the edges of the base inclined at 45° to
the V.P.
PROJECTION OF SOLID
Problem 4 : Draw the projections of a hexagonal pyramid, base 30 mm side and axis 60
mm long, having its base on the H.P. and one of the edges of the base inclined at 45° to
the V.P.
PROJECTION OF SOLID
Axis perpendicular to the V.P.:
Problem 5 : A hexagonal prism has one of its rectangular faces parallel to the H.P. Its axis
is perpendicular to the V.P. and 3.5 cm above the ground.
Draw its projections when the nearer end is 2 cm in front of the V.P. Side of base 2.5 cm
long; axis 5 cm long.
PROJECTION OF SOLID
Problem 5 : A hexagonal prism has one of its rectangular faces parallel to the H.P. Its axis
is perpendicular to the V.P. and 3.5 cm above the ground.
Draw its projections when the nearer end is 2 cm in front of the V.P. Side of base 2.5 cm
long; axis 5 cm long.
