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= 1 centimetre cube

Volumes by Counting Cubes. Volume is the amount of space a 3D - shape takes up. 1cm. 1cm. 1cm. One Unit of Volume is the “CUBIC CENTIMETRE”. = 1 centimetre cube. = 1 cm³. Volumes by Counting Cubes.

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= 1 centimetre cube

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  1. Volumes by Counting Cubes Volume is the amount of space a 3D - shape takes up 1cm 1cm 1cm One Unit of Volume is the “CUBIC CENTIMETRE” = 1 centimetre cube = 1 cm³

  2. Volumes by Counting Cubes This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³? 1cm 1cm 1cm 1cm = 2 cm³ = 2 centimetre cubes

  3. 1cm 1cm Volumes by Counting Cubes This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³ 1cm 1cm = 3 centimetre cubes = 3 cm³

  4. Volumes by Counting Cubes One unit of Volume is the “CUBIC CENTIMETRE” 3cm 2cm 4cm Volume = 24 centimetre cube = 24 cm³

  5. 4cm 3cm 6cm A short cut ! height Area of rectangle breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume= length x breadth x height

  6. Heilander’s Porridge Oats Example 1 Working Volume = l x b x h V = 18 x 5 x 27 V = 2430 cm³ 27cm 5 cm 18 cm

  7. Example 2 Working Volume = l x b x h V = 2 x 2 x 2 V = 8 cm³ 2cm

  8. Liquid Volume I’m a very small duck! How much water does this hold? 1 cm 1 cm 1 cm Volume = x b x h l = 1 cm³ A cube with volume 1cm³ holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre.

  9. Orange Flavour Example 1 Liquid Volume Working Volume = l x b x h V = 6 x 3 x 12 12 cm V = 216 cm³ = 216 ml 3 cm 6 cm So the carton can hold 216 ml of orange juice. How much juice can this carton hold? Remember: 1 cm³ = 1 ml

  10. Example 2 Working Liquid Volume Volume = l x b x h 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.

  11. Revision of Area The Rectangle The RAT The Square b h l b l l

  12. Don’t forget the faces edges and corners we can’t see at the back Face Edges and Vertices The shape below is called a cuboid. It is made up of FACES, EDGES and VERTICES. Edges are where the two faces meet (lines) Vertices where lines meet (corners) Faces are the sides of a shape (surface area)

  13. Calculate the number of faces edges and vertices for a cuboid. Face Edges and Vertices 6 faces 12 edges Front and back are the same 8 vertices Top and bottom are the same Right and left are the same

  14. Calculate the number of faces edges and vertices for a cube. Face Edges and Vertices 6 faces 12 edges Faces are squares 8 vertices

  15. Calculate the number of faces, edges and vertices for these shapes Face Edges and Vertices 5 faces 9 edges 6 Vertices 2 faces 1 edges 1 Vertices Cone Triangular Prism Cylinder Sphere 3 faces 2 edges 1 faces 0 Vertices 0 edges 0 Vertices

  16. Surface Area of the Cuboid What is meant by the term surface area? The complete area of a 3D shape

  17. Example Find the surface area of the cuboid Working 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 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

  18. Example Find the surface area of the cuboid Working Front Area = l x b = 8 x 6 =48cm2 Top Area = l x b = 8 x 5 =40cm2 6cm Side Area = l x b = 6 x 5 =30cm2 5cm Total Area = 48+48+40+40+30+30 = 236cm2 8cm Frontandbackare the same Topandbottomare the same Right andleftare the same

  19. Volume of Solids Definition : A prism is a solid shape with uniform cross-section Hexagonal Prism Cylinder (circular Prism) Triangular Prism Pentagonal Prism Volume = Area of Face x length

  20. Any Triangle Area h = vertical height b Sometimes called the altitude h 20

  21. Any Triangle Area 8cm Example 1 : Find the area of the triangle. 6cm Area = 24cm²

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

  23. Triangle Area = 4cm 10cm 4cm Volume of a Triangular Prism Working = 2 x4 = 8 cm2 Volume = Area x length = 8 x 10 = 80cm3 Find the volume of the triangular prism

  24. Triangle Area = 6cm Example Find the volume of the triangular prism. Working = 3 x 3 = 9 cm2 Volume = Area x length = 9 x 30 = 270cm3 3cm 30cm Total Area = 6+6+30+40+50 = 132cm2

  25. Triangle Area = 4cm Example Find the surface area of the right angle prism Working = 2 x3 =6cm2 Rectangle 1 Area = l x b = 3 x10 =30cm2 5cm Rectangle 2 Area = l x b 3cm 10cm = 4 x 10 =40cm2 Rectangle 3 Area = l x b = 5 x 10 =50cm2 2 triangles the same 1 rectangle 3cm by 10cm Total Area = 6+6+30+40+50 = 132cm2 1 rectangle 4cm by 10cm 1 rectangle 5cm by 10cm

  26. Triangle Area = 4cm 10cm 4cm Surface Areaofa Triangular Prism Working = 2 x4 = 8 cm2 5cm Rectangle 1 Area = l x b = 5 x10 =50cm2 Rectangle 2Area = l x b = 5 x10 =50cm2 2 triangles the same Rectangle 3 Area = l x b 2 rectangle the same 5cm by 10cm = 4 x 10 =40cm2 1 rectangle 4cm by 10cm Total Area = 8+8+50+50+40 = 156cm2

  27. Volume of a Cylinder 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 Cylinder (circular Prism) = πr2h

  28. Volume of a Cylinder Example : Find the volume of the cylinder below. 5cm V = πr2h 10cm = π(5)2x10 Cylinder (circular Prism) = 250π cm

  29. Surface Area of a Cylinder 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 2 x Circles Rectangle Total Surface Area = 2πr2 + 2πrh

  30. Surface Area of a Cylinder Example : Find the surface area of the cylinder below: 3cm Surface Area = 2πr2 + 2πrh 10cm = (2 x π x 3²)+ (2 x π x3 x10) = 2 x π x 9 + 2 x π x 30 Cylinder (circular Prism) = 245.04cm²

  31. Surface Area of a Cylinder Radius = 1diameter 2 Example : A net of a cylinder is given below. Find the curved surface area only! 6cm Curved Surface Area = 2πrh = 2 x π x 3 x 9 9cm = 169.64 cm2

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