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Revision of Area Revision of Volume and Surface Area Volume of a Prism Volume & Surface Area of Solids www.mathsrevision.com Volume of a Cylinder Volume.

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Presentation on theme: "Revision of Area Revision of Volume and Surface Area Volume of a Prism Volume & Surface Area of Solids www.mathsrevision.com Volume of a Cylinder Volume."— Presentation transcript:

1 Revision of Area Revision of Volume and Surface Area Volume of a Prism Volume & Surface Area of Solids Volume of a Cylinder Volume of a Pyramid Curved Area of a Cylinder Volume of a Sphere Exam Type Questions

2 Tuesday, 14 April Created by Mr.Lafferty Starter Questions Q1.True or false Q2.Write down the probability of picking out a number greater than 20 in the national lottery. Q3.If a = -3 and b = -4 does Q4.Calculate a 2 – 3b 2 = 57

3 Revision of Areas Trapezium Rhombus and kite Parallelogram Any Type of Triangle Circle Level 4

4 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know formulae. 1.We are revising area of basic shapes. 2.Use formulae correctly. 3.Show working and appropriate units. appropriate units. Area Level 4

5 Tuesday, 14 April Created by Mr.Lafferty Area Example : Find the area of the V – shape kite. 7cm 4cm Level 4

6 Tuesday, 14 April Created by Mr.Lafferty Composite Areas We can use our knowledge of the basic areas to work out more complicated shapes. 4cm 3cm 5cm 6cm Example : Find the area of the arrow. Level 4

7 Tuesday, 14 April Created by Mr.Lafferty Composite Areas Example : Find the area of the shaded area. 11cm 10cm 8cm 4cm Level 4

8 14-Apr-15 Created by Mr. Lafferty Maths Dept. The Circle Example : Find the area of the shape 20cm 5 cm Area = rectangle + semicircle Composite Areas Level 4

9 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.1 Ch16 (page 121) Area 9 Level 4

10 Tuesday, 14 April Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Find the area of the triangle. Q2.Expand out and simplify 2w 2 – 3(2w – 5) Q4.Rearrange into the form y = 2y – 3x + 7 = 0 4cm 3cm 10cm

11 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Know formulae. 1.We are revising volume and surface area of a cuboid. 2.Use formulae correctly. 3.Show working and appropriate units. appropriate units. Volume & Surface Area Level 4

12 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid 4 layers of 18 cubes = 4 x 18= 72 centimetre cubes= 72 cm³ 18 cubes fit the base. = 1 centimetre cube = 1 cm³ 3cm 4cm 6cm Level 4

13 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. A short cut ! 6 = 72 cm³ Volume =length x breadth x 4 x height length breadth height x 3Volume = 3cm 4cm 6cm Area of rectangle Level 4

14 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Volume = l x b x h V = 18 x 5 x 27 V = 2430 cm³ Example 18 cm 5 cm 27cm Heilander’s Porridge Oats Working Level 4

15 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Example 2cm Volume = l x b x h V = 2 x 2 x 2 V = 8 cm³ Working Level 4

16 10 cm 9 cm 8 cm 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Example Find the volume of the composite shape. V 1 = l x b x h = 3 x 5 x 7 = 105 cm³ 7 cm 3 cm 5 cm V 2 = l x b x h = 8 x 10 x 9 = 720 cm³ V T = V 1 + V 2 V T = V T = 825 cm 3 Level 4

17 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Volume = L x B x H 200 = L x 5 x = 20L Example Find the length the cuboid 5 cm 4 cm 10 cm V=200cm 3 This just an equation. We know how to solve them ! 20L = 200 L = 10 L Level 4

18 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Example 50 cm 100 cm 30 cm Volume = l x b x h V = 100 x 30 x 50 V = cm³ = ml So the fish tank can hold 150 litres of water. How much water can this fish tank hold in litres? 1cm 3 = 1 ml 1000 ml = 1 litre = 150 litres Working Liquid Volume Level 4

19 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Face Edges and Vertices The shape below is called a cuboid. It is made up of FACES, EDGES and VERTICES. Faces are the sides of a shape (surface area) Edges are where the two faces meet (lines) Vertices where lines meet (corners) Level 4 Don’t forget the faces edges and corners we can’t see at the back

20 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Face Edges and Vertices Front and back are the same Top and bottom are the same Right and left are the same 6 faces 12 edges 8 vertices Level 4 Calculate the number of faces edges and vertices for a cuboid.

21 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Face Edges and Vertices Faces are squares 6 faces 12 edges 8 vertices Level 4 Calculate the number of faces edges and vertices for a cube.

22 14-Apr-15 Compiled by Mr. Lafferty Maths Dept. Front Area = l x b = 5 x 4 =20cm 2 Example Find the surface area of the cuboid Working 5cm 4cm 3cm Top Area = l x b = 5 x 3 =15cm 2 Side Area = l x b = 3 x 4 =12cm 2 Total Area = = 94cm 2 Front and back are the same Top and bottom are the same Right and left are the same Level 4

23 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.2 Ch16 (page 122) Volume & Surface Area 23 Level 4

24 Tuesday, 14 April Created by Mr.Lafferty Starter Questions Q1.True or false 2(x – 6) - 2(x + 6) = 0 Q2.Does x 20 = Explain your answer Q3.Factorise 2y 2 + 3y +2 Q4.Calculate

25 Learning Intention Success Criteria 1.We are learning how to calculating volume of any prism given area. 1. Calculate the volume for various prisms. 2. Solution must include appropriate units and working. appropriate units and working. Volume of Prisms Level 4

26 Definition : A prism is a solid shape with uniform cross-section Cylinder (circular Prism) Pentagonal Prism Triangular Prism Hexagonal Prism Volume = Area of Cross section x length Level 4 Volume of Prisms

27 Definition : A prism is a solid shape with uniform cross-section Cylinder (circular Prism) Pentagonal Prism Triangular Prism Hexagonal Prism Volume = Area of Cross section x length Level 4 Volume of Prisms

28 Definition : A prism is a solid shape with uniform cross-section Triangular Prism Volume = Area x length Q. Find the volume the triangular prism. 20cm 2 10cm = 20 x 10 = 200 cm 3 Volume of Solids

29 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.3 Ch16 (page 124) 29 Level 4 Volume of Prisms

30 Tuesday, 14 April Created by Mr.Lafferty Starter Questions Q1.Find the area of the parallelogram Q2.Factorise 4x + 40 Q3.A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4.The speed of light is metres per sec. True or false in scientific notation 3 x

31 Learning Intention Success Criteria 1.To know formula. 1.We are learning how to derive the formula for the volume of a cylinder and apply it to solve problems. 2.Apply formula correctly. 3.Work backwards using formula. Volume of a Cylinder Level 4

32 Volume = Area x height The volume of a cylinder can be thought as being a pile of circles laid on top of each other. = πr 2 Volume of a Cylinder Cylinder (circular Prism) x h h = πr 2 h Level 4

33 V = πr 2 h Example : Find the volume of the cylinder below. = π(5) 2 x 10 5cm Cylinder (circular Prism) 10cm = 250π cm 3 Volume of a Cylinder = cm 3

34 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.4 Ch16 (page 125) 34 Level 4 Volume of a Cylinder

35 Tuesday, 14 April Created by Mr.Lafferty Starter Questions Q1.Factorise Q2.Write down the probability of picking out a number less than 30 in the national lottery. Q3.True or false if a = -1 and b = -2 Q4.Explain why -(a 2 ) + b 2 = 5

36 Learning Intention Success Criteria 1.To know formula. 1.We are learning how to use the formula for the volume of ANY pyramid and apply it to solve problems. 2.Apply formula correctly. 3.Work backwards using formula. Volume of a Pyramid Level 4

37 The volume of any pyramid can be calculated using the formula Volume of a Pyramid Level 4 A = Area of base h = height cone

38 Q. Find the volume the pyramid. 100m 2 Volume of Pyramid 12m Level 4

39 Q.If the above cone has radius 15cm and height of 10 cm.Calculate it’s volume. Volume of a Cone Level 4 r h

40 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.5 Ch16 (page 127) 40 Level 4 Volume of a Pyramid

41 Tuesday, 14 April Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Expand out and simplify 3(x – 2) - ( - 3x + 4) Q2.Factorise 2x 2 – 16x Q4.By rearranging in y =, find the gradient and where the straight line crosses the x-axis y + 4x - 3 = 0

42 Learning Intention Success Criteria 1.To know how to split up a cylinder. 1.We are learning how to calculate the surface area of a cylinder by using basic areas. 2.Calculate the surface area of a cylinder. Surface Area of a Cylinder Level 4

43 Total Surface Area = 2πr 2 + 2πrh The surface area of a cylinder is made up of 2 basic shapes can you name them. Curved Area =2πrh Cylinder (circular Prism) h Surface Area of a Cylinder Roll out curve side  2πr Top Area =πr 2 Bottom Area =πr 2 Level 4

44 Example : Find the surface area of the cylinder below: = 2π(3) 2 + 2π x 3 x 10 3cm Cylinder (circular Prism) 10cm = 18π + 60π Surface Area of a Cylinder Surface Area = 2πr 2 + 2πrh = 245 cm 2 Level 4

45 Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. D= Surface Area of a Cylinder D = 25 25cm 9cm 25 π Diameter = 2r Surface Area = 2πr 2 + 2πrh = 2π(3.98) 2 + 2π(3.98) x 9 = = cm 2 = 7.96 cm

46 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.6 Ch16 (page 129) Surface Area of a Cylinder 46 Level 4

47 Tuesday, 14 April Created by Mr.Lafferty Q3.Calculate Starter Questions Q1.Find the area of the triangle. Q2.Factorise 4x 2 – 64x Q4.Rearrange equation in y = y – 2x + 5 = 0 6cm 10cm

48 Learning Intention Success Criteria 1.To know the volume formula for a sphere. 1.We are learning how to use the sphere formula and use it to solve real-life problems. 2.Work out volumes for spheres. 3.Answer to contain appropriate units and working. appropriate units and working. Level 4 Volume of Solids

49 Volume of a Sphere Level 4 r D D = diameter Q.If the above sphere has radius 10cm. Calculate it’s volume.

50 Level 4 Q. Find the volume the composite shape. Volume = Cylinder + half a sphere h = 6m r 2m ½ sphere Cylinder Volume of a sphere

51 Tuesday, 14 April 2015 Created by Mr. Now try TJ 4+ Ex 16.7 Ch16 (page 130) Volume of a sphere 51 Level 4

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