Maharashtra Board Class 6 Maths part 2 Chapter 18 Three Dimensional Shapes PDF Download

Three Dimensional Shapes

Cuboids Or Rectangular Prisms

All the faces of a cuboid are rectangular and its opposite faces are identical or congruent. The cuboid is also a quadrangular prism. How many edges does the cuboid have? How many vertices does it have? How many faces does it have?

In the figure here, points A and B are two of the eight vertices. Seg AB and seg AP are the names of two edges and ABCD is the name of one face.

A cuboid has 12 edges, 8 vertices and 6 faces.

Teacher's Note

A cuboid is like a box. Your math book is a cuboid. It has 6 flat sides, 8 corners and 12 edges.

Exam Trick

Remember: Cuboid = Box shape. A cube has all sides equal. A cuboid has different lengths, widths and heights.

Points to Remember

A cuboid has 6 rectangular faces.
A cuboid has 8 vertices or corners.
A cuboid has 12 edges or sides.

Cubes

There is a dice in the figure alongside. What difference do you see in the shape of a dice and that of a cuboid? When all the faces of a quadrangular prism are equal squares, it is called a cube.

How many faces does a cube have?

How many edges does a cube have?

How many vertices does a cube have?

Teacher's Note

A cube is like a dice. All six faces are the same size squares. Your sugar cubes at home are cubes.

Exam Trick

Remember: Cube = all sides equal. Cuboid = sides not equal. Cube is a special cuboid.

Points to Remember

A cube has 6 square faces.
All faces of a cube are the same size.
A cube has 8 vertices and 12 edges just like a cuboid.

Triangular Prisms

What is the shape of the faces at the base and at the top of the figure alongside?

What is the shape of the faces on the sides?

Such a figure is called a triangular prism.

How many edges, vertices and faces does a triangular prism have?

Teacher's Note

A triangular prism has a triangle base. Toblerone chocolate is shaped like a triangular prism.

Exam Trick

Remember: Triangular prism has two triangular faces. The other three faces are rectangles.

Points to Remember

A triangular prism has 5 faces.
It has 2 triangular faces and 3 rectangular faces.
It has 6 vertices and 9 edges.

Cylinders

You must have seen a tall box with a circular base. A tin like this is a familiar example of a cylinder. If the tin is closed, it is a closed cylinder. A closed cylinder has two flat circular faces and one curved face. The cylinder has two circular edges and no vertex.

Give some examples of cylinders you are familiar with.

Take a rectangular sheet. Bring together its opposite sides. A hollow cylinder will be formed.

Take a cylindrical tin. Take a rectangular sheet with one side equal to the height of the tin. Wrap it around the tin to cover it completely and cut away the extra paper. Then unfold it and spread it out on a table.

Take another sheet. Place the box on it and draw its circular outline. Cut away the paper around it. Cut out another circle like this one. Place these discs next to the rectangular paper as shown in the figure above. The figure obtained is the net of the closed cylinder. Make a cylinder using this net.

Teacher's Note

A cylinder is like a tin box. A drinking glass without handles is a cylinder. Pencils are also cylinder shaped.

Exam Trick

Remember: Cylinder = two circles + one rectangle. No corners or vertices in a cylinder.

Points to Remember

A cylinder has 2 circular flat faces and 1 curved face.
A cylinder has 2 circular edges.
A cylinder has no vertices or corners.

Pyramids

When playing carrom, you make a pile of the pieces as shown in the picture. What is the shape of this pile?

If you place a number of CDs or round biscuits one on top of the other, what shape do you get?

A net is shown here. It has identical triangular sides. Draw a figure like this on a card-sheet and cut it out. Fold along the dotted lines of the square and bring the sides together so that the vertices A, B, C and D meet at a point.

You will get a shape like the one shown below. Its base is a square and its other standing faces are triangles.

This shape is called a pyramid. The top or apex of this shape is pointed like a needle. As the base of this shape is a quadrilateral, it is called a quadrangular pyramid. Count the edges, vertices and faces of this shape.

A quadrangular pyramid has 5 faces, 8 edges and 5 vertices.

Draw the net shown alongside on a card-sheet and cut it out. Fold along the dotted lines of the triangle in the centre and bring together the triangles on the sides so that the vertices A, B and C meet at a point. You will get a pyramid. The base of this pyramid is a triangle. Hence, it is called a triangular pyramid.

Count and write the number of its edges, vertices and faces.

Teacher's Note

A pyramid is like a mountain top. The Egyptian pyramids are pyramid shaped. A cone is like an ice-cream cone.

Exam Trick

Remember: Pyramid = pointed top + base shape. Triangular pyramid has 3 sides. Quadrangular pyramid has 4 sides.

Points to Remember

A quadrangular pyramid has 5 faces, 8 edges and 5 vertices.
A triangular pyramid has 4 faces, 6 edges and 4 vertices.
The top point is called the apex.
All sides except the base are triangles.

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