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

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

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

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

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

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

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

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

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

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Example 2 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

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Revision of Area l l l bh b The SquareThe Rectangle The RAT

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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) Don’t forget the faces edges and corners we can’t see at the back

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

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

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

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

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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

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Front Area = l x b = 8 x 6 =48cm 2 Example Find the surface area of the cuboid Working 8cm 6cm 5cm Top Area = l x b = 8 x 5 =40cm 2 Side Area = l x b = 6 x 5 =30cm 2 Total Area = = 236cm 2 Front and back are the same Top and bottom are the same Right and left are the same

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

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

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

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

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Volume of a Triangular Prism 4cm 10cm = 2 x4 = 8 cm 2 Working Volume = Area x length = 8 x 10 = 80cm 3 Triangle Area = Find the volume of the triangular prism

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Example Find the volume of the triangular prism. Total Area = = 132cm 2 3cm 6cm 30cm = 3 x 3 = 9 cm 2 Working Volume = Area x length = 9 x 30 = 270cm 3 Triangle Area =

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

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

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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

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

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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 Rectangle 2 x Circles

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

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

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