Common Solids - Mathematics Form 1 Notes

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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
     common solids sphere
     no faces, edges or corners  sphere examples
     Cylinder
    cylinder solids
     2 circular bases connected by a curved surface  

    cylinder examples

     Cube
    cube solids
     6 square faces, 12 edges and 8 corners; all sides equal  cube examples
     Cone
    cone solids
     round base with a curved surface that forms a point  Cone example
     Rectangular prism
    rectangular prism
     6 faces with opposite faces being equal, 12 edges and 8 corners  rectangular prism example
     Pyramid
    pyramid solids
     square base and 4 triangular faces, 8 edges and 5 corners  pyramid example


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


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
    cube net
  2. Cuboid net
    cuboid net
  3. Triangular prism net
    triangular prism net
  4. Pentagonal prism
    pentagonal prism
  5. Square base pyramid
    square based pyramid
  6. Cylinder net
    cylinder net

  7. Cone net
    cone net
  8. Hexagonal prism
    hexagonal prism
  9. Tetrahedron
    tetrahedron
  10. Octahedron
    octahedron
  11. Dodecagon
    dodecagon

Example

An ant moved from Y to X the midpoint of RS through P in the right pyramid below
right pyramid example
Draw the net of the pyramid showing the path of the ant hence find the distance it moved.

Solution

solution right pyramid

Distance=15 + √(144+16)
=27.649cm

Example

Draw the net of the solid below.

net of solid

Solution

net of solid 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.
    common solids q1
    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.
    common solids q2
  3. The figure below represents below represents a prism of length 7 cm AB = AE = CD = 2 cm and BC – ED = 1 cm.
    common solids q3
    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.
    comon solids q4
    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)
    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)
  5. The figure below shows a solid regular tetrapack of sides 6 cm
    common solids q6
    1. Draw a net of the solid
    2. Find the surface area of the solid
  6. The figure below shows a solid made by pasting two equal regular tetrahedral
    common solids q7
    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.
    1. Sketch the net of the prism shown below
      common solids q8
    2. Find the surface area of the solid
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Read 3265 times Last modified on Monday, 17 January 2022 11:53
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