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Volume of Right Prisms

In this worksheet students will learn the formula for finding the volume of various right prisms and apply them to find the volume.

'Volume of Right Prisms' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Volume and Surface Area Calculations

Difficulty level:  

Worksheet Overview

A prism is a shape which has the same cross-section throughout its height.

By this I mean if you cut a prism, it may get smaller but the overall shape stays the same.

Here are some examples




If you sliced through the cross-section of these shapes, they would get smaller but the overall shape would stay the same.

Cross-sections of the shapes above are a circle, triangle, square and rectangle

The cross-section is the shape of the face of the prism.


How do I find the volume? They are all different shapes.

Ah yes, yet another formula to learn. 


Volume of a prism = area of the cross-section x height




 Before we continue we need a recap of how to find the area of these shapes.



Area of a square = base x height



Area of a rectangle = base x height



Area of a triangle = base x height ÷ 2




Area of a circle =  π x r x r


Can you remember the value of π?  Don't worry you will find out later if you have forgotten.


Almost there.  To find the volume we calculate the area of the face first and then multiply by the height.


 Time to practice.


Find the volume of this box of chocolates. Base = 6 cm.

The face  (cross-section) is a square - find the area first.

 6 x 6 = 36 cm, now just multiply by the length, which as its a square box  is also 6 cm.   36 x 6 = 216 cm³


Find the volume of the cornflakes box.  Base 12 cm, height 6 cm, length 30 cm

The face  (cross-section) is a rectangle - find the area first. 

12 x 6 = 72 cm, now just multiply by the length   72 x 30 = 2160 cm³



Find the volume of the triangular prism.  Base 4 cm, height 4 cm, length 12 cm

The face  (cross-section) is a triangle - find the area first. 

4 x 4 = 16 ÷ 2; = 8 cm, now just multiply by the length 8 x 12 = 96 cm³




Find the volume of this can.  Radius 4 cm, length 8 cm.


The face  (cross-section) is a circle - find the area first. 

Did you remember the value of π, of course, 3.142

Area = 3.142 x 4 x 4 = 50.27

Now multiply by length 50.27 x 8 = 402.16 cm³



That was a bit of a marathon, wasn't it?  Guess what, it is not over...

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