By studying this lesson, you will be able to,
prepare models of a cube, cuboid and regular tetrahedron,
identify and state the shapes of the faces of these solids and the
number of faces, edges and vertices each solid has, and
create various nets to prepare models of the above mentioned
solids and create new compound solids with these models.
The following figure illustrates several items that we see and use in our day to day activities.
An object of specific shape which occupies a certain amount of space is called a solid object.
Now let us consider the surfaces, faces, edges and vertices of several solids.
Every solid has an outer surface which is called the “surface” of the solid.
The faces of solids
You may have realized from the above activity that the outer surface of solids consists of different shaped plane surface parts and/or curved surface parts.
The edges of solids
A boundary along which two surface parts of a solid meet is called an edge of the solid.
The vertices of solids
Let us consider solids such as a brick or a die. The place where three or more edges of such a solid meet is called a vertex.
(1) Complete the following table by considering the number of edges, vertices and surface parts each solid consists of.
All the surface parts of a die are plane surfaces. All
its faces take the shape of a square and are of equal
size. A solid object such as a die, with all its faces
square shaped and of equal size, is said to be the
shape of a cube.
Step 3 - Draw the following figure on a square ruled paper.
Step 4 - Cut out the figure that you drew and either copy it or paste it on a thick piece of paper such as a Bristol board.
Step 5 - Cut out the figure on the thick piece of paper and by folding along the relevant lines and pasting down the shaded allowances, prepare a model of a cube.
Step 6 - Examine the shape of a face, and determine the number of faces, the number of edges, the number of vertices and other special properties of the model you prepared. Write down the properties you identified in your exercise book.
Without the pasting allowances, the above figure which was used to create a model of a cube is a net of the cube.
Step 7 - In your square ruled exercise book, draw two other nets that can be used to prepare a model of a cube.
The properties you can identify in a cube.
● A cube has 6 faces. The shape of each face is a square.
● All the faces of a cube are identical to each other.
● A cube has 12 edges. All 12 edges are rectilinear.
● A cube has 8 vertices.
(1) From the following figures, select the nets that can be used to create cubes and draw them in your exercise book.
(2) Write down two solid objects which take the shape of a cube.
(3) A portion of a net that can be used to make a cube is given in the figure. Complete the net and draw it in your exercise book.
(4) Draw a suitable net to prepare a cube of side length 3 cm.
Step 1 – Draw the figure given here on a square ruled piece of paper. Copy or paste this on a piece of Bristol board.
Step 2 – Make a model of a cuboid by cutting the figure on the Bristol board, folding it appropriately and pasting along the allowances.
Step 3 – Measure and write down the length, breadth and height of the model you created.
Step 4 – Examine the model that you made, and identify the shapes of the faces of the cuboid, the number of faces, edges and vertices and any other special properties.
Step 5 – Write down the properties that you identified in your exercise book.
Without the pasting allowances, the above figure which was used to create a model of a cuboid is a net of the cuboid.
Step 6 – In your exercise book, draw another net that can be used to prepare a model of a cuboid.
(1) Name five objects that you can observe in your environment which take the shape of a cuboid.
(2)
(i) Draw a figure of a cuboid in your square ruled exercise book.
(ii) Measure and write down the length, breadth and height of the cuboid that was drawn.
(3) Write down the length, breadth and height of the cuboid that can be made with the net in the figure.
(4) The figure illustrates a part of a net drawn to make a cuboid. Complete it and draw it in your square ruled exercise book.
(5) It is required to make a cuboid of length 10 cm, breadth 6 cm and height 4 cm. Draw a net for the above cuboid and mark its measurements, by assuming that the length of 1 square of a square ruled page is 1 cm.
Now let us identify properties of a regular tetrahedron which is a solid object, by doing the following activity.
Step 4 - Cut out the figure, fold it appropriately along the straight lines and by pasting down the allowances, make a model of a solid.
Step 5 - Identify the shape of the model, the shape of its faces, the number faces, edges and vertices and any other special properties.
Step 6 - Write down the properties that you identified in your exercise book.
Step 7 - Measure the lengths of the edges of the model.
Step 8 - Draw another net that can be used to prepare a model of a regular tetrahedron.
What you made in the above activity is a model of a tetrahedron. All its faces are equal and all its edges too are equal. Therefore it is a regular tetrahedron.
(1) What is the shape of a face of a regular tetrahedron?
(2) What is the length of an edge of the model of a regular tetrahedron that can be made using the net given in the figure?
(3) The figure depicts a net which can be used to make a model of a regular tetrahedron. What is the length of an edge of the regular tetrahedron that can be made using this net?
(4) Draw a suitable net to create a model of a regular tetrahedron with edges of length 6 cm (Draw one triangle of the net on a tissue paper and using it prepare the net).
It is possible to construct a compound solid by combining together some of the solids that you have already identified.
(1) A compound solid is made by placing the cube in the figure on an identical cube, such that two of the faces coincide, and then pasting them together.
(i) What is the name of the solid that is made?
(ii) Write down the measurements of the solid.
(2) A solid has been made by placing two identical regular tetrahedrons together, such that two of their faces coincide, and then pasting these two faces together. For this compound figure, write down
(i) the number of faces.
(ii) the number edges.
(iii) the number of vertices.
