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Revision of Area

Volume & Surface Area of Solids. Revision of Area. Revision of Volume and Surface Area. Volume of a Prism. Volume of a Cylinder. www.mathsrevision.com. Volume of a Pyramid. Curved Area of a Cylinder. Volume of a Sphere. Exam Type Questions. Starter Questions. Q1. True or false.

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Revision of Area

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

  2. Starter Questions Q1. True or false Q2. Write down the probability of picking out a number greater than 20 in the national lottery. www.mathsrevision.com Q3. If a = -3 and b = -4 does a2 – 3b2 = 57 Q4. Calculate Created by Mr.Lafferty

  3. Revision of Areas Level 4 Rhombus and kite Any Type of Triangle www.mathsrevision.com Circle Parallelogram Trapezium

  4. Area Level 4 Learning Intention Success Criteria • Know formulae. • We are revising area of basic shapes. • Use formulae correctly. www.mathsrevision.com • Show working and • appropriate units. Compiled by Mr. Lafferty Maths Dept.

  5. Area Level 4 Example : Find the area of the V – shape kite. 4cm www.mathsrevision.com 7cm Created by Mr.Lafferty

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

  7. Composite Areas Level 4 Example : Find the area of the shaded area. 8cm 11cm www.mathsrevision.com 4cm 10cm Created by Mr.Lafferty

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

  9. Area Level 4 Now try TJ 4+ Ex 16.1 Ch16 (page 121) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  10. Starter Questions 10cm Q1. Find the area of the triangle. 3cm 4cm Q2. Expand out and simplify 2w2 – 3(2w – 5) www.mathsrevision.com Q3. True or false Q4. Rearrange into the form y = 2y – 3x + 7 = 0 Created by Mr.Lafferty

  11. Volume & Surface Area Level 4 Learning Intention Success Criteria • Know formulae. • We are revising volume and surface area of a cuboid. • Use formulae correctly. www.mathsrevision.com • Show working and • appropriate units. Compiled by Mr. Lafferty Maths Dept.

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

  13. 4cm 3cm 6cm A short cut ! Level 4 height Area of rectangle breadth www.mathsrevision.com length Volume = 6 x 3 x 4 = 72 cm³ Volume = length xbreadth x height Compiled by Mr. Lafferty Maths Dept.

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

  15. Example Working Volume = l x b x h Level 4 V = 2 x 2 x 2 V = 8 cm³ 2cm www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

  16. Example Find the volume of the composite shape. Level 4 VT = V1 + V2 7 cm VT = 105 + 720 5 cm VT = 825 cm3 3 cm 9 cm V1 = l x b x h www.mathsrevision.com = 3 x 5 x 7 V2 = l x b x h = 105 cm³ 10 cm = 8 x 10 x 9 8 cm = 720 cm³ Compiled by Mr. Lafferty Maths Dept.

  17. Example Find the length the cuboid This just an equation. We know how to solve them ! Level 4 4 cm Volume = L x B x H V=200cm3 200 = L x 5 x 4 5 cm www.mathsrevision.com 200 = 20L 10 cm L 20L = 200 L = 10 Compiled by Mr. Lafferty Maths Dept.

  18. Example Working Liquid Volume Volume = l x b x h Level 4 V = 100 x 30 x 50 V = 150 000 cm³ 50 cm = 150 000 ml = 150 litres 30 cm 100 cm 1cm3 = 1 ml 1000 ml = 1 litre How much water can this fish tank hold in litres? So the fish tank can hold 150 litres of water. Compiled by Mr. Lafferty Maths Dept.

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

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

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

  22. Example Find the surface area of the cuboid Working Level 4 Front Area = l x b = 5 x 4 =20cm2 Top Area = l x b = 5 x 3 =15cm2 4cm Side Area = l x b = 3 x 4 =12cm2 3cm www.mathsrevision.com Total Area = 20+20+15+15+12+12 = 94cm2 5cm Front and back are the same Top and bottom are the same Right and left are the same Compiled by Mr. Lafferty Maths Dept.

  23. Volume & Surface Area Level 4 Now try TJ 4+ Ex 16.2 Ch16 (page 122) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  24. Starter Questions Q1. True or false 2(x – 6) - 2(x + 6) = 0 Q2. Does 2.5 + 1.25 x 20 = 27.55 Explain your answer www.mathsrevision.com Q3. Factorise 2y2 + 3y +2 Q4. Calculate Created by Mr.Lafferty

  25. Volume of Prisms Level 4 Learning Intention Success Criteria • 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. www.mathsrevision.com

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

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

  28. Volume of Solids Definition : A prism is a solid shape with uniform cross-section Q. Find the volume the triangular prism. www.mathsrevision.com Triangular Prism Volume = Area x length = 20 x 10 = 200 cm3 10cm 20cm2

  29. Volume of Prisms Level 4 Now try TJ 4+ Ex 16.3 Ch16 (page 124) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  30. Starter Questions Q1. Find the area of the parallelogram 7 7 Q2. Factorise 4x + 40 www.mathsrevision.com Q3. A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4. The speed of light is 300000000 metres per sec. True or false in scientific notation 3 x 108. Created by Mr.Lafferty

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

  32. Volume of a Cylinder Level 4 The volume of a cylinder can be thought as being a pile of circles laid on top of each other. Volume = Area x height h = πr2 x h www.mathsrevision.com Cylinder (circular Prism) = πr2h

  33. Volume of a Cylinder Example : Find the volume of the cylinder below. 5cm V = πr2h 10cm www.mathsrevision.com = π(5)2x10 Cylinder (circular Prism) = 250π cm3 = 784.5 cm3

  34. Volume of a Cylinder Level 4 Now try TJ 4+ Ex 16.4 Ch16 (page 125) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  35. Starter Questions Q1. Factorise Q2. Write down the probability of picking out a number less than 30 in the national lottery. www.mathsrevision.com Q3. True or false if a = -1 and b = -2 -(a2)+ b2 = 5 Q4. Explain why Created by Mr.Lafferty

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

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

  38. Volume of Pyramid Level 4 Q. Find the volume the pyramid. 12m 100m2 www.mathsrevision.com

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

  40. Volume of a Pyramid Level 4 Now try TJ 4+ Ex 16.5 Ch16 (page 127) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  41. Starter Questions Q1. Expand out and simplify 3(x – 2) - ( - 3x + 4) Q2. Factorise 2x2 – 16x www.mathsrevision.com Q3. True or false Created by Mr.Lafferty

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

  43. Surface Area of a Cylinder Level 4 The surface area of a cylinder is made up of 2 basic shapes can you name them. Cylinder (circular Prism) Curved Area =2πrh 2πr Top Area =πr2 h Roll out curve side  Bottom Area =πr2 www.mathsrevision.com Total Surface Area = 2πr2 + 2πrh

  44. Surface Area of a Cylinder Level 4 Example : Find the surface area of the cylinder below: 3cm Surface Area = 2πr2 + 2πrh 10cm = 2π(3)2 +2πx 3 x 10 www.mathsrevision.com = 18π + 60π Cylinder (circular Prism) = 245 cm2

  45. Surface Area of a Cylinder Diameter = 2r Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. C = 25 25 9cm 25cm www.mathsrevision.com D = = 7.96 cm π Surface Area = 2πr2 + 2πrh = 2π(3.98)2 + 2π(3.98)x9 = 99.5 + 225 = 324.5 cm2

  46. Surface Area of a Cylinder Level 4 Now try TJ 4+ Ex 16.6 Ch16 (page 129) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  47. Starter Questions Q1. Find the area of the triangle. 10cm Q2. Factorise 4x2 – 64x 6cm www.mathsrevision.com Q3. Calculate Q4. Rearrange equation in y = y – 2x + 5 = 0 Created by Mr.Lafferty

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

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

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

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