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Example 1

Draw a right hexagonal prism with height 5 cm and length of one side of the hexagon = 2.5 cm.

Solution :

Example 2

When is a cuboid a cube ?

Solution :

If the length, breadth and height of a cuboid are equal it is a cube.

Example 3

What is the difference between a right prism and an oblique prism ?

Solution :

In a right prism, the angle formed by the lateral edges with the planes containing the bases is 900. In oblique prism the same angle is not 900 . In oblique prism the same angle is not 900 .

Example 4

What is the altitude of a prism ?

Solution :

A prism has two congruent polygons joined together at their corresponding vertices. The perpendicular distance between the two polygons is the height of the prism. It is hence obvious that in a right prism the length of the lateral side is the altitude of the prism.

Example 5

If the volume of a cube is 27. Find the surface area.

Solution :

Volume of a cube    = cube of its length

= l3

= 27

Since   l 3     = 27

                

                  l = 3

Surface area of a cube      =    6 l 2

= 6 (3)2

= 6 ´ 9

= 54 sq. units

Example 6

If the height of a cuboid is zero it becomes a (a) prism (b) cube (c) rectangle.

Solution :

A cuboid is two congruent rectangles that are separated from each other by a distance = height. If the height is zero these two will collapse on each other to form one rectangle.

The other two options i.e. prism and cube are obviously wrong because both cannot have height = zero.

Index

8.1 Introduction to solid geometry
8.2 Prism
8.3 The cuboid and the cube
8.4 Cylinders
8.5 Pyramids
8.6 Right circular cone
8.7 Sphere

Chapter 9

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