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Volume of prisms

Tutor: Labib

# Volume of prisms

## In a nutshell

The volumes of various 3D shapes can be calculated by using their respective formulae.

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## Prisms

### ​​Definition

A prism is a 3D shape that is a 2D shape stretched in the third dimension. The 2D shape is called it's cross-section.

##### Examples

 This is a prism with a cross-section that is a hexagon. Therefore, this shape is called a hexagonal prism. This is a prism with a cross-section that is a triangle. Therefore, this shape is called a triangular prism. A cylinder is also a type of prism, it has a circular cross-section.

## Formulae for volumes of 3D shapes

Here are the 3D shapes that you need to be able to calculate the volumes of:

 SHAPE FORMULA DIAGRAM Cube ​$V=x\times x\times x=x^3$​​ Where $x$ is the length of a single side. Cuboid ​$V=\text{length}\times\text{width}\times\text{height}$​​ ​$V=lwh$​​ Cylinder ​$V=\pi \times \text{radius}^2\times \text{height}$​​ ​$V=\pi r^2 h$​​ Prism $V=A\times l$​​ Where $A$​ is the area of the cross-section, and $l$ is the length.

##### Example

A prism has a cross-sectional area of $7.5cm^2$ and a length of $12cm$. What is the volume of the prism?

Substitute $A=7.5$ and $l=12$ into the formula:

\begin{aligned}V&=A\times l\\&=7.5\times12\\&=90\end{aligned}

The volume of the prism is $\underline{90cm^3}$.

## FAQs - Frequently Asked Questions

### What is a prism?

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