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Characteristics of planes & solids Ar. Surashmie Kaalmegh Asisstant Professor LAD College , Nagpur
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Characteristics of planes & solids
Ar. Surashmie Kaalmegh Asisstant Professor LAD College , Nagpur
In the subject we learn …
Orthographic projections
Interpenetration
Development of solids.
Scales
Isometric projections
Perspective view
Drawing elements
Point Line Plane Colour Texture
Points
Planes :
Some basics :
Lines & Planes :
Regular Solids
Characteristics
Faces / Surfaces
Edges
Vertices
Each face is a plane ……
Construction of a Solid
Solids have volumes…
The pyramid :
A pyramid is a three-dimensional figure with a single base and a three or more non-parallel sides that meet at a single point above the base. The sides of a pyramid are triangles.
A regular pyramid is a pyramid that has a regular polygon for its base and
whose sides are all congruent triangles.
Properties of a Regular Pyramid The edges of a regular pyramid are
equal; it is denoted by e. The lateral faces of a regular pyramid
are congruent isosceles triangles . The altitudes of the lateral faces of a
regular pyramid are equal. It is the slant height of the regular pyramid and is denoted by L.
The altitude of the regular pyramid is perpendicular to the base. It is equal to length of the axis and is denoted by h.
The vertex of regular pyramid is directly above the center of its base when the pyramid is oriented as shown in the figure.
If a cutting plane is passed parallel to the base of regular pyramid, the pyramid cut off is a regular pyramid similar to the original pyramid.
Cone :
The slant height of a right circular cone is the length of an element. Both the slant height and the element are denoted by L.
The altitude of a right circular is the perpendicular drop from vertex to the center of the base. It coincides with the axis of the right circular cone and it is denoted by h.
If a right triangle is being revolved about one of its legs (taking one leg as the axis of revolution), the solid thus formed is a right circular cone.
The surface generated by the hypotenuse of the triangle is the lateral area of the right circular cone and the area of the base of the cone is the surface generated by the leg which is not the axis of rotation.
All elements of a right circular cone are equal.
Any section parallel to the base is a circle whose center is on the axis of the cone.
A section of a right circular cone which contains the vertex and two points of the base is an isosceles triangle.
Properties of a Cone An element of a cone is the
generator in any particular position.
The altitude of the cone is the perpendicular drop from vertex to the plane of the base. It is denoted as h.
Every section of a cone made by a plane passing through its vertex and containing two points of the base is a triangle. See section PQV, where V is the vertex and P and Q are two points on the base.
The axis of the cone is the straight line joining the vertex with the centroid of the base.
For right cone, altitude and axis are equal in length.
The right section of a cone is a section perpendicular to its axis and cutting all the elements. For right cone, the right section is parallel and similar to the base. Right section is denoted by AR.
A circular cone is cone whose right section is a circle.
Complex solids :
