CLASS 7TH | UNIT 4: GEOMETRY | RECOGNISITION OF SOLIDS(REPRESENTING- 3D IN 2D) | REVISION NOTES

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

1. 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

2. 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.

1. Slicing and Cutting: It gives the cross-sectional view of a solid. 
2. Shadow Casting: It gives 2D2D view of an 3D3D object.
3. 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:

1. Take a squared paper.
2. Draw the front face.
3. Draw the opposite face of the same size.
4. Join the corresponding corners.
5. Draw the figure with hidden edges dotted.