To find the volume of different prisms, you can use simple formulas based on the shape of the base.

A prism has a shape that is the same all the way through, extending in one direction.

1. General Formula for Volume

The general formula for the volume ( V ) of any prism is:

[ V = B \cdot h ]

Here:

• ( B ) is the area of the base,
• ( h ) is the height (or length) of the prism.

2. Volume of Rectangular Prisms

For rectangular prisms (also called cuboids), the base is a rectangle.

If the base has a length ( l ) and a width ( w ), the area of the base is:

[ B = l \times w ]

So, the volume of a rectangular prism is:

[ V = l \times w \times h ]

3. Volume of Triangular Prisms

For triangular prisms, the base is a triangle.

If the base has a base length ( b ) and a height ( t ), the area is:

[ B = \frac{1}{2} \times b \times t ]

Then, the volume of a triangular prism is:

[ V = \frac{1}{2} \times b \times t \times h ]

4. Volume of Other Prisms

For other shapes:

• For a hexagonal prism, you can find the base area using the formula for a hexagon, and then use the general volume formula.
• Always make sure that the height is straight up from the base for correct answers.

Conclusion

By learning these formulas, Year 7 students can find the volume of different prisms. This helps them improve their math skills and understand geometry better.