Volume Part 1

Volume Part 1

The volume of a prism.

Today's Learning Aims:

• Knowledge: Learning the formula for calculating the volume of a prism.

• Understanding: Being able to correctly interpret the formula for calculating the volume of a prism.

• Skills: The ability to apply the formula to effectively calculate the volume of a prism.

Multiple Choice

Calculate the volume of this cube:

• $9m^3$

• $81m^3$

• $27m^3$

• $30m^3$

Multiple Choice

Calculate the volume of this shape assuming it is made up of four identical cubes.

•  $1024cm^3$  

•  $128cm^3$  

•  $64cm^3$  

•  $256cm^3$  

Multiple Choice

Calculate the volume of this shape assuming it is made up of four identical cubes.

• $4000m^3$

• $625m^3$

• $500m^3$

• Not Enough Information Provided

3D Shapes

• 3-dimensional (3D) shapes are solid shapes with three dimensions: length, width and height.

• 3D shapes have faces, edges and vertices.

• A face is a flat surface.

• An edge it where two faces meet.

• A vertex is a corner where edges meet, the plural is vertices.

Cross-Section

The cross-section is the shape we get when cutting straight through an object. In geometry it is the shape made when a solid is cut through by a plane.

See the figure for some examples of a 3D shape being cut by a plane.

The Volume of a Prism

• A prism is a solid (3D) object which is the same shape all the way through i.e. it has a constant area of cross-section known as a uniform cross-section.

• The volume of a prism is equal to its cross-sectional area multiplied by its length.

• See the adjacent figure for some examples of prims.

When the Area of the Cross-Section is Known

• When the area of a prism's cross-section is known you simply multiply this by the prism's length to calculate it's volume.

• The volume of a prism =        cross-sectional area  $\times$  length

Multiple Choice

What is the volume of this prism?

• $45m^3$
  

• $90m^3$
  

• $45cm^3$

• $180m^3$

Sometimes the area of the cross-section is not given and then then we have to calculate it.

• You will need to use your prior knowledge of calculating areas in these situations.

• See the adjacent figure for a summary of key area formulae.

Volume of a Triangular Prism

Volume of a prism 
= Area of Cross-Section  $\times$  length

Worked Example:

 $Volume=\frac{5}{2}\times2\times4$  

 $Volume\ =\ 20cm^3$  

Volume of a Cuboid

Volume =  width  $\times$  length  $\times$  height

Worked Example:

  $Volume=2\times4\times3$  

 $Volume=24cm^3$  

Multiple Choice

What is the volume of the cuboid?

• 160cm³

• 184cm³

• 40cm²

• 200cm³

Volume of a Cylinder

 $Volume\ of\ a\ cylinder$  

 $=\pi r^2\times length$  

Worked Example: 

 $Volume=\pi\times\left(\frac{7}{2}\right)^2\times16$  
 $Volume=615.8cm^3\ \left(to\ 1\ decimal\ place\right)$  

Multiple Choice

What is the volume of this cylinder?

•  $282.7cm^{3\ }$  

•  $94.2cm^3$  

•  $1131.0cm^3$  

•  $365cm^3$  

Important Things to Remember When Calculating Volume

• All the dimensions must be in the same units, for example

   $meter\times meter\times meter$   

• Volume is measured in cubic units, for example  $m^3$ or  $cm^3$ . Always remember to include the correct unit when stating a volume.      

Now It's Your Turn

• Activity 1: Complete Worksheet 1, this has been shared in the Google Classroom work stream under the heading Volume.

• Activity 2: Complete Worksheet 2, this has been shared in the Google Classroom work stream under the heading Volume.

• Activity 3: Extension Task, some challenging problems involving volume.

Multiple Choice

What is the volume of the prism?

• $400mm^3$

• $100mm^3$

• $200mm^3$

• $300mm^3$

Multiple Choice

• 3cm

• 3.5cm

• 4cm

• 4.5cm

Multiple Choice

What is the volume of this prism?

• $21cm^3$
  

• $36cm^3$
  

• $18cm^3$
  

• $60cm^3$

Multiple Choice

What is the volume of this prism?

• 80cm³

• 32cm³

• 40cm³

• 20cm³

Poll

What task did you get onto today?

• Worksheet 1

• Worksheet 2

• Extension Task

• Completed all three activities.

Closing Comments

• If you have any questions please email me, [e-mail]

• See you Lesson 4 on Monday.