Plane Figures and Solid Shapes:
- Plane figures are flat or 22-Dimension figures, they have no thickness.
- For example: Squares, rectangles, circles, triangles etc.
- Solid Shapes are 33-Dimension shapes, and they occupy space and have volume.
- For example: Cube, cuboid, sphere, cone, hemisphere etc.
Faces, Edges and Vertices of 3D3D Shapes:
- A 3D3D shapes is not flat therefore it has 33 dimensions and these are faces, edges, and vertices.
- Faces: It is simply the face of a 3D3D shape or the flat surface of the 3D3D shape
- For example: The number of faces of a cube is 66.
- Edges: They are the line segments which join one vertex to another vertex.
- For example – Edges in a cylinder are 22 and are shown below.
- Vertices: Points where two or more edges meet between faces are known vertices of any 3D3D shape or the corners of 3D3D shape.
- For example: The cube has 88 vertices and is shown below
Net for building 3D3D Shapes:
- Net is used for making 3D3D shapes.
- It is a basic skeleton outline in 22-Dimensions i.e., it is a flat 33-Dimensional shape which can be folded and joined together with the help of glue.
- Nets for building some shapes are shown below
Drawing Solids on a Flat Surface:
- There are two ways of drawing solids on a flat surface
- Oblique Sketches:
- It is an easy way of representing the 3D3D objects in pictorial form.
- These sketches are intended to show the perspective of 3D3D object and are drawn on a sheet by freehand.
- It does not talk about the measurement of 3D3D object
- Oblique sketch of cube is shown below
- Isometric Sketches:
- It is also the pictorial representation of a 3D3D objects, but it also meets with measurements of the 3D3D object to be drawn.
- It is drawn on isometric sheets.
- Isometric sketch of cube is shown below and the dotted sheet on which the sketch is made is known as isometric sheet
Viewing Different Sections of a Solid
- There are many methods to view different sections of a solid.
- Slicing and Cutting: It gives the cross-sectional view of a solid.
- Shadow Casting: It gives 2D2D view of an 3D3D object.
- Viewing Solid from Different Angle: The front-view, the side-view and the top-view are the most common ways to view a solid; it can provide a lot of information about the shape
Solid: An object that occupies space and has a fixed space is called solid.
Some of the characteristics of a solid are:
- Solids have length, breadth and height. It is a three-dimensional figure.
- Solid objects have only three main views.
- Top view.
- Side view.
- Front view.
Cuboid:
Cuboid is solid or hollow which has 6 rectangular faces.
- It is a three dimensional solid.
- A cuboid has 12 edges.
- A cuboid has 8 vertices.
Cube:
Cube is a symmetrical three-dimensional shape, either solid or hollow contained by six equal squares.
- Each face of a cube is square.
- Cube has 6 faces.
- Cube has 12 edges.
- Cube has 8 corners.
Cylinder:
Cylinder is a solid or hollow geometrical figure with a curved side and two identical circular flat ends.
- Cylinder has 2 edges, 3 faces but no vertex.
Sphere:
Sphere is a round solid or hollow figure with every point on its surface equidistant from its centre.
- A sphere is a 3D figure with no vertex, no edges and only1 surface.
Cone:
Cone is a solid or hollow object which tampers from a circular base to a point.
- Cone is a 3D figure with 1 vertex, 1 edge and 2surfaces.
Prism:
Prism is a solid geometrical figure whose two ends are similar, equal and parallel rectilinear figures and whose sides and faces are either parallelograms or rectangles.
- It has 3 faces,9 edges, and 6 vertices.
- Prism is a solid whose side faces are ||gm and whose end basses are two parallel and congruent polygons.
Pyramid:
Pyramid is a solid whose base is a plane rectilinear figure such as triangle and whose side faces are triangles with a common vertex.
- If the base of the pyramid is quadrilateral then it is called a quadrilateral pyramid.
- If the base of the pyramid is triangle then it is called a triangular pyramid.
Euler’s formula:
For a 3-D solid,
- V stands for the number of vertices.
- E stands for the number of edges.
- F stands for the number of faces.
Euler’s formula is V + F – E = 2.
Drawing a cube:
- The two types of sketches for drawing a cube are oblique and isometric.
- An isometric paper has dots or lines, marked on it dividing the paper into small equilateral triangles.
Cube:
Steps:
- Take a squared paper.
- Draw the front face.
- Draw the opposite face of the same size.
- Join the corresponding corners.
- Draw the figure with hidden edges dotted.
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