Common Solids - Mathematics Form 1 Notes

• Introduction
• Sketching Solids
  • Use of Isometric Projections
• Past KCSE Questions on the Topic

Introduction

• A solid is an object which occupies space and has a definite or fixed shape. Solids are either regular or irregular.
  

  Shape	Characteristics	Real Life Examples
  Sphere	no faces, edges or corners
  Cylinder	2 circular bases connected by a curved surface
  Cube	6 square faces, 12 edges and 8 corners; all sides equal
  Cone	round base with a curved surface that forms a point
  Rectangular prism	6 faces with opposite faces being equal, 12 edges and 8 corners
  Pyramid	square base and 4 triangular faces, 8 edges and 5 corners

  
  
  Note:
• Intersections of faces are called edges.
• The point where three or more edges meet is called a vertex.
  
  

Sketching Solids

• To draw a reasonable sketch of a solid on a plan paper,the following ideas are hepful:

Use of Isometric Projections

In this method the following points should be obtained:

• Each edge should be drawn to the correct length.
• All rectangular faces must be drawn as parallelograms.
• Horizontal and vertical edges must be drawn accurately to scale.
• The base edges are drawn at an angle 300with the horizontal lines.
• Parallel lines are drawn parallel.

Examples

1. Cube net
   
   
2. Cuboid net
   
   
3. Triangular prism net
   
   
4. Pentagonal prism
   
   
5. Square base pyramid
   
   
6. Cylinder net
   
   
   
7. Cone net
   
   
8. Hexagonal prism
   
   
9. Tetrahedron
   
   
10. Octahedron
    
    
11. Dodecagon
    
    

Example

An ant moved from Y to X the midpoint of RS through P in the right pyramid below

Draw the net of the pyramid showing the path of the ant hence find the distance it moved.

Solution

Distance=15 + √(144+16)
=27.649cm

Example

Draw the net of the solid below.

Solution

B1 B1 B1

Scale drawing Correct labeling Correct measurement of GJ and FI

Past KCSE Questions on the Topic

1. The figure below shows a net of aprism whose cross – section is an equilateral triangle.
   
   
   1. Sketch the prism
   2. State the number of planes of symmetry of the prism.
2. The figure below represents a square based solid with a path marked on it. Sketch and label the net of the solid.
   
   
3. The figure below represents below represents a prism of length 7 cm AB = AE = CD = 2 cm and BC – ED = 1 cm.
   
   Draw the net of the prism (3 marks)
4. The diagram below represents a right pyramid on a square base of side 3 cm. The slant of the pyramid is 4 cm.
   
   
   1. Draw a net of the pyramid (2 marks)
   2. On the net drawn, measure the height of a triangular face from the top of the Pyramid  (1 mark)
      
5. 1. Draw a regular pentagon of side 4 cm (1 mark)
      
   2. On the diagram drawn, construct a circle which touches all the sides of the pentagon (2 marks)
6. The figure below shows a solid regular tetrapack of sides 6 cm
   
   
   1. Draw a net of the solid
   2. Find the surface area of the solid
7. The figure below shows a solid made by pasting two equal regular tetrahedral
   
   
   1. Draw a net of the solid
      
   2. If each face is an equilateral triangle of side 5cm, find the surface area of the solid.
8. 1. Sketch the net of the prism shown below
      
      
   2. Find the surface area of the solid