1. 1 Volume: Lesson Objectives Understand the meaning of Volume Recognise the shapes of Prisms Determine the volume of Prisms

2. 2 What Is Volume ? The volume of a solid is the amount of space inside the solid. Consider the cylinder below: If we were to fill the cylinder with water the volume would be the amount of water the cylinder could hold

3. 3 Measuring Volume. Volume is measured in cubic centimetres (also called centimetre cubed). Here is a cubic centimetre It is a cube which measures 1cm in all directions. 1cm We will now see how to calculate the volume of various prisms.

4. Key concepts of Volume of Prisms 4 A Prism Cylinder Cuboid Triangular Prism Trapezoid Prism Volume of Prism = length x Cross-sectional area Cross section

5. Key concepts of Volume of Prisms 5 Area Formulae r h b b h h b a h b b a b Area Circle = π x r 2 Area Rectangle = Breadth x Height Area Trapezium = ½ x (a + b) x h Area Triangle = ½ x Base x height

6. Key concepts of Volume of Prisms 6 Volume Cube Prism 5.3cm 7.2cm 10.6cm Cross-sectional Area = B x H = 7.2 x 5.3 = 38.16cm 2 DO NOT ROUND! Volume = Length x Cross-sectional Area = 10.6 x 38.16 = 404.5cm 3 USE ‘ANS’! Note that there are 3 dimensions so the units are cubic m or cm.

7. 7 What Goes In The Box ? You Try! Calculate the volumes of the cuboids below: (1) 14cm 5 cm 7cm (2) 3.4cm (3) 8.9 m 2.7m 3.2m 76.9 m 3 490cm 3 39.3cm 3

8. Key concepts of Volume of Prisms 8 Volume Triangular Prism 8.6cm 6.2cm 4.1cm Cross-sectional Area = ½ x b x h = ½ x 8.6 x 4.1 DO NOT ROUND! = 17.63cm 2 Volume = length x Cross-sectional Area = 17.63 x 6.2 = 109.3cm 3 USE ‘ANS’! Note that there are 3 dimensions so the units are cubic m or cm.

9. Key concepts of Volume of Prisms 9 Volume Trapezoid Prism 1.7cm 8.2cm 6.3cm 4.9cm Cross-sectional Area = ½ x(a + b) x h = ½ x (6.3 + 1.7) x 4.9 DO NOT ROUND! = 19.6cm 2 Volume = length x Cross-sectional Area = 8.2 x 19.6 = 160.7cm 3 USE ‘ANS’! Note that there are 3 dimensions so the units are cubic m or cm.

10. The Volume Of A Cylinder. Consider the cylinder below: 4cm 6cm It has a height of 6cm. What is the size of the radius ? 2cm Volume = cross section x height What shape is the cross section? Circle Calculate the area of the circle: A =  r 2 A = 3.14 x 2 x 2 A = 12.56 cm 2 Calculate the volume: V =  r 2 x h V = 12.56 x 6 V = 75.36 cm 3 The formula for the volume of a cylinder is: V =  r 2 h r = radius h = height.

11. 11 What Goes In The Box ? 2 You Try. Calculate the volume of the shapes below: (1) 16cm 14cm (2) 3m 4m 5m (3) 6cm 12cm 8m 2813.4cm 3 30m 3 288cm 3

12. More Complex Shapes. Calculate the volume of the shape below: 20m 23m 16m 12m Calculate the cross sectional area: A1 A2 Area = A1 + A2 Area = (12 x 16) + ( ½ x (20 –12) x 16) Area = 192 + 64 Area = 256m 2 Calculate the volume: Volume = Cross sectional area x length. V = 256 x 23 V = 2888m 3

13. Calculate the volume of the shape below: 12cm 18cm 10cm Calculate the cross sectional area: A2 A1 Area = A1 + A2 Area = (12 x 10) + ( ½ x  x 6 x 6 ) Area = 120 +56.52 Area = 176.52cm 2 Calculate the volume. Volume = cross sectional area x Length V = 176.52 x 18 V = 3177.36cm 3 Example 2.

14. What Goes In The Box ? 3 18m 22m 14m 11m (1) 23cm 32cm 17cm (2) 4466m 3 19156.2cm 3

15. Volume Of A Cone. Consider the cylinder and cone shown below: The diameter (D) of the top of the cone and the cylinder are equal. D D The height (H) of the cone and the cylinder are equal. H H If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ? 3 times. This shows that the cylinder has three times the volume of a cone with the same height and radius.

16. The experiment on the previous slide allows us to work out the formula for the volume of a cone: The formula for the volume of a cylinder is : V =  r 2 h We have seen that the volume of a cylinder is three times more than that of a cone with the same diameter and height. The formula for the volume of a cone is: h r r = radius h = height

17. Calculate the volume of the cones below: 13m 18m (2)9m 6m (1)

18. Summary Of Volume Formula. l b h V = l b h r h V =  r 2 h b l h V = ½ b h l h r