1. We are learning to: - Enhance our Mathematical learning skills * solve volume problems Vocabulary: cross section cubic unit Always aim high! LESSON OBJECTIVES Be Responsible Independent Learner Positive Thinker

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. 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 shapes.

4. For the solids below identify the cross sectional area required for calculating the volume: Circle (2) Right Angled Triangle. (3) Pentagon (4) A2 A1 Rectangle & Semi Circle. (1)

5. For the solids below identify the cross sectional area required for calculating the volume: Circle (2) Right Angled Triangle. (3) Pentagon (4) A2 A1 Rectangle & Semi Circle. (1)

6. 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.

7. The Volume Of A Triangular Prism. Consider the triangular prism below: Volume = Cross Section x Height What shape is the cross section ? Triangle. Calculate the area of the triangle: 5cm 8cm 5cm A = ½ x base x height A = 0.5 x 5 x 5 A = 12.5cm 2 Calculate the volume: Volume = Cross Section x Length V = 12.5 x 8 V = 100 cm 3 The formula for the volume of a triangular prism is : V = ½ b h l B= base h = height l = length

8. What Goes In The Box ? 2 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

9. 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

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

11. We are learning to: - Enhance Mathematical basic skills knowledge. -Accurately calculate the volume of a pyramid. Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Reflective Learner

12. 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

13. 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

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

15. Effective Participator Self Manager Reflective Learner Volume of Pyramids EXAMPLES Volume of a pyramid = x base area x vertical height Calculate the volume of the pyramids below: (a)(b) Base area = 7cm x 4cm = 28cm 2 Volume of a pyramid = x base area x vertical height = x 28 x 6 = 56cm 2 Base area = 20cm x 13cm = 260cm 2 Volume of a pyramid = x base area x vertical height = x 260 x 12 = 1040cm 2

16. TASK (Grade B) EXTENSION 1 1)2) 1) 2) Square base