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 $$\underline{90cm^3}$$.