To find the volume of prisms, we need to know a simple formula that works for all kinds of prisms.

What is a Prism?

A prism is a shape that has two identical ends (called bases) connected by rectangular sides.

Formula for Prisms

The volume ( V ) of a prism can be calculated using this formula: [ V = B \times h ] Where:

• ( B ) is the area of the base
• ( h ) is the height of the prism (the straight distance between the two bases)

Types of Prisms

1. Rectangular Prism

   • Area of the Base: ( B = l \times w ) (where ( l ) is the length and ( w ) is the width)
   • Volume: [ V = l \times w \times h ]

2. Triangular Prism

   • Area of the Base: [ B = \frac{1}{2} \times b \times h_b ] (where ( b ) is the base of the triangle and ( h_b ) is the height of the triangle)
   • Volume: [ V = \frac{1}{2} \times b \times h_b \times h ]

3. Pentagonal Prism

   • Area of the Base: For a regular pentagon with a side length ( s ): [ B = \frac{1}{4} \sqrt{5(5 + 2\sqrt{5})} s^2 ]
   • Volume: [ V = B \times h ]

Important Facts

• Prisms can be different shapes, like rectangular, triangular, or hexagonal. Each shape means we calculate the base area in different ways.

• The height ( h ) is very important because if you double the height, you also double the volume.

• Units are important in calculating volume. If the base area is in square units (like ( cm^2 )) and the height is in linear units (like ( cm )), then the volume will be in cubic units (like ( cm^3 )).

Applications

Knowing how to find the volume of prisms is useful in many real-life situations. This includes things like building, packaging, and storing liquids. Understanding these calculations can help us in our everyday lives.