Maharashtra Board Class 5 Maths Part Two Chapter 13 Three Dimensional Objects and Nets PDF Download

Three Dimensional Objects and Nets

Two Dimensional Drawings of Three Dimensional Objects

Tai pointed to an object on a slightly high table and asked.

Tai: What is that?

Sharad: That's a card which has a nice picture of laddoos.

Tai: Since you're looking at it from the front, it appears to be a card. Let me turn it around a little and put it on the floor.

Sheela: I thought it was just a nice picture on a card. But the picture is actually pasted on a box.

Tai: At first, you only saw the front surface. Now, when you look from above and from a different angle, you can see three different surfaces and you can also see that it is actually a three dimensional box.

Sharad: What does three dimensional mean?

Tai: Three dimensional objects are objects whose length, width and height can be seen, felt or measured. Books, glasses and tables are some three dimensional objects. Objects which have only length and breadth and no thickness or negligible thickness can be called two dimensional objects. Sheets of paper, pictures on paper and shadows are some examples of two dimensional figures.

Sheela: Actually, objects are three dimensional. Their pictures on paper are two dimensional.

Sharad: That is why, some pictures seem flat. But some pictures are drawn in such a way that we can sense the depth or thickness of the objects.

Tai: Let me show you a chart. It shows how three dimensional objects appear when seen from the front, from the side and from above. Study it carefully.

Teacher's Note

When you look at your school cupboard from the front, you see the doors. But when you look from the side, it looks different. When you see it from above, it looks like a rectangle. This is how we see different views of three dimensional objects.

Exam Trick

Remember: Three dimensional means length, width, and height. Two dimensional means only length and breadth. When a teacher asks "How many views can you see?", always think of three views - front, side, and above.

Points to Remember

Three dimensional objects have length, width, and height.

Two dimensional objects have only length and breadth.

The same object looks different from the front, side, and above.

Pictures on paper are two dimensional, but real objects are three dimensional.

Looking at hills in the distance, we can see how tall and broad they are. But, we cannot tell how much area they occupy on the ground. One has to go up and above them in a helicopter to see how much area they occupy on land. But then, from there we cannot see how high they are. Therefore, to show the area over which a hill is spread and also how high it is in its different parts, two figures like those below are drawn.

In figure 1, we see hills as from a distance. The lines show their approximate heights. Figure 2 shows the extent of land they occupy as seen from above and the curved lines show their different heights in different parts. For example, the line that shows 800m indicates a height of about 800m.

In Geography, such diagrams are used to show mountains on maps.

Teacher's Note

When you see a mountain from far away, you can see how high it is. But when you see it from above in a helicopter, you can see how much land it covers. Both views are important and useful.

Exam Trick

Remember: From front = see height. From above = see area covered. If a question asks about how much land a mountain covers, think "from above" view.

Points to Remember

We see height and shape from the front view of a hill.

We see area covered from the top view.

Curved lines on a map show different heights.

Geographic diagrams help us understand mountains better.

Problem Set 51

1. The first column shows a structure made of blocks. The other columns show different views of the structure in two dimensions. Say whether each view is from the front, from a side or from above.

2. Draw three pictures of each of these three dimensional objects - a table, a chair and a water-bottle as viewed from the front, from a side and from above.

Nets

Last year we saw that cutting some edges of a box and laying it out flat gives us the net from which it was made.

The two dimensional shape from which a three dimensional object can be made by folding is called the 'net' of that object.

(1) By folding the cardboard shown below, along the lines shown in it, we get a three dimensional object (box). In this shape, all surfaces are square.

An object of this shape is called a cube.

(2) The net of another cardboard box is shown in the figure below. By folding along the lines in this net and joining the edges to each other, we can see that a three dimensional box is formed. The surfaces of this box are rectangular in shape.

An object of this shape is called a cuboid.

Activity: Draw the nets shown below on card sheet. Cut out the shapes and find out the shapes of the boxes they form.

Teacher's Note

A net is like an unfolded box. When you open a pizza box and lay it flat, that is a net. When you fold it back, it becomes the box again. Nets help us understand how three dimensional shapes are made.

Exam Trick

Remember: Net = flat shape. Fold the net = three dimensional object. If you are confused, draw the net on paper, cut it, and fold it to see what shape it makes.

Points to Remember

A net is a two dimensional shape that folds into a three dimensional object.

A cube has all square surfaces.

A cuboid has rectangular surfaces.

You can cut and fold nets to make boxes and understand shapes better.

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