CLASS 6TH | UNIT 4: GEOMETRY | RECOGNISITION OF SOLIDS | REVISION NOTES

You come across many solids every day. The football that you play, the book that you read, the LPG cylinder used for cooking and so on are all solids. Unlike 2D shapes, a solid has length, breadth and depth.

In this chapter, you will learn about solids and recognition of various solid shapes.

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.