Rectangular prisms

Introduction

To find out how much concrete is needed to pour the footpath in this photo you need to know how to calculate the volume of a rectangular prisim.

Photo of a footpath boxed and ready for concrete to be poured.

Do you know how to calculate the volume of rectangular prisms?

Image of a rectangular prisim with a length of 2 m, height of 1 m  and width of 1 m.

Calculating volume

The formula for calculating volume is: 
Volume = Area by height 
V = A X h

The formula for calculating area of a rectangle is: 
Area = length by width 
A = l X w

So the volume of a rectangular prism can be calculated using the formula: 
Volume = length by width by height 
V = l X w X h

For the rectangular prism in the diagram: 
V = 2 m X 1 m X 1 m 
V = 2 m³ (cubic metres)

Image of a rectangular prisim with a length of 2 m, height of 1 m  and width of 2 m.

Exercise 1

Calculate the volume of this rectangular prism.

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Image of a rectangular prisim with a length of 3 m, height of 3 m  and width of 2 m.

Exercise 2

Calculate the volume of this rectangular prism.

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   Submit

 

Image of a rectangular prisim with a length of 6 m, height of 4 m  and width of 3 m.

Exercise 3

Calculate the volume of this rectangular prism.

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Image of a rectangular prisim with a length of 5 m, height of 3.5 m  and width of 2.5 m.

Exercise 4

Calculate the volume of this rectangular prism.

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Image of a rectangular prisim with a length of 3500 mm, height of 2700 mm  and width of 2400 mm.

Exercise 5

Calculate the volume of this rectangular prism (measurements in millimetres).

Before doing calculations convert millimetres to metres.

Length = 3.5 m 
Width = 2.4 m 
Height = 2.7 m

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Image of a rectangular prisim with a length of 3500 mm, height of 2700 mm  and width of 2400 mm.

Exercise 6

Calculate the volume of this rectangular prism (measurements in millimetres).

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Shapes made of combined rectangular/square prisms

Image of a shape made up of of combined rectangular prisms.

To calculate the volume of this shape you can break it into two rectangular prisms (RP1 and RP2).

Select this link to see RP1 and RP2.

Method to use:

Volume total = Volume RP1 plus Volume RP2 
Vt = V RP1 + V RP2 
Vt = (l X w X h) + (l X w X h) 
Vt = (2 X 1 X 1) + (1 X 1 X 1) 
Vt = 3 + 1 
Vt = 3 m³.

 

 

Image of a shape made up of of combined rectangular prisms.

Exercise 7

Calculate the volume of this object.

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Type in your answer and select submit for feedback.

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Image of a shape made up of of combined rectangular prisms.

Exercise 8

Calculate the volume of this object.

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Type in your answer and select submit for feedback.

   Submit

 

Image of a shape made up of of combined rectangular prisms.

Exercise 9

Calculate the volume of this object.

Select this link for a hint.

Type in your answer and select submit for feedback.

   Submit

 

Summary

This is the end of the section on Rectangular prisms.

Key points to remember are: 

  • the formula for volume is:
    Volume = Area by height
  • volume of a rectangular prism is calculated using the formula:
    Volume = length by width by height
  • break combined rectangular/square prisms into individual prisms
  • calculate the volume of each prism, then add the volumes together.

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