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Volume of prisms

Volume of prisms

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Explainer Video

Tutor: Labib

Summary

Volume of prisms

In a nutshell

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


​​

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



Maths; Measures; KS3 Year 7; Volume of prisms

Maths; Measures; KS3 Year 7; Volume of prisms

Maths; Measures; KS3 Year 7; Volume of prisms


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×x×x=x3V=x\times x\times x=x^3V=x×x×x=x3​​


Where xxx is the length of a single side.
Maths; Measures; KS3 Year 7; Volume of prisms

Cuboid

​V=length×width×heightV=\text{length}\times\text{width}\times\text{height}V=length×width×height​​


​V=lwhV=lwhV=lwh​​
Maths; Measures; KS3 Year 7; Volume of prisms

Cylinder

​V=π×radius2×heightV=\pi \times \text{radius}^2\times \text{height}V=π×radius2×height​​


​V=πr2hV=\pi r^2 hV=πr2h​​
Maths; Measures; KS3 Year 7; Volume of prisms

Prism

V=A×lV=A\times lV=A×l​​


Where AAA​ is the area of the cross-section, and lll is the length.
Maths; Measures; KS3 Year 7; Volume of prisms


Example

A prism has a cross-sectional area of 7.5cm27.5cm^27.5cm2 and a length of 12cm12cm12cm. What is the volume of the prism?


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

​V=A×l=7.5×12=90\begin{aligned}V&=A\times l\\&=7.5\times12\\&=90\end{aligned}V​=A×l=7.5×12=90​​


The volume of the prism is 90cm3‾\underline{90cm^3}90cm3​.


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Learn with Basics

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Length:
Formulae for the area and volume of shapes

Unit 1

Formulae for the area and volume of shapes

Calculating the volume of cubes and cuboids

Unit 2

Calculating the volume of cubes and cuboids

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Optional

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Volume of prisms

Unit 3

Volume of prisms

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FAQs - Frequently Asked Questions

What is the formula for the volume of a cuboid?

The volume of a cuboid is length x width x height.

What is the formula for the volume of a prism?

The volume of a prism can be found by multiplying the area of its cross-section by its length.

What is a prism?

A prism is a 3D shape that is a 2D shape stretched into the third dimension.

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