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**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

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**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 centimetre cubes = 2 cm³

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**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 = 3 centimetre cubes = 3 cm³

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**Volumes by Counting Cubes**

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

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**A short cut ! Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth**

height Area of rectangle breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height

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**Example 1 27cm 5 cm 18 cm Working Volume = l x b x h V = 18 x 5 x 27**

Heilander’s Porridge Oats V = 18 x 5 x 27 V = cm³ 27cm 5 cm 18 cm

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

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**Liquid Volume Volume = l x b x h = 1 cm³**

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

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**Example 1 Working Volume = l x b x h V = 6 x 3 x 12 V = 216 cm³**

Liquid Volume Working Orange Flavour 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

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**Example 2 Working Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³**

Liquid Volume Working Volume = l x b x h V = 100 x 30 x 50 V = cm³ 50 cm = ml = 150 litres 30 cm 100 cm How much water can this fish tank hold in litres? 1cm3 = 1 ml 1000 ml = 1 litre So the fish tank can hold 150 litres of water.

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

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**Face Edges and Vertices**

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) Faces are the sides of a shape (surface area) Vertices where lines meet (corners)

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**Face Edges and Vertices**

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

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**Face Edges and Vertices**

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

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**Face Edges and Vertices**

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

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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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**Find the surface area of the cuboid**

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 5cm Total Area = = 94cm2 Front and back are the same Top and bottom are the same Right and left are the same

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**Find the surface area of the cuboid**

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 8cm Total Area = = 236cm2 Front and back are the same Top and bottom are the same Right and left are the same

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**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

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**Sometimes called the altitude**

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

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**Any Triangle Area Example 1 : Find the area of the triangle. 6cm**

Area = 24cm²

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**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

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**Volume of a Triangular Prism**

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

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**Find the volume of the triangular prism.**

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

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**Find the surface area of the right angle prism**

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

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**Surface Areaof a Triangular Prism**

Working Triangle Area = = 2 x4 = 8 cm2 5cm Rectangle 1 Area = l x b 4cm = 5 x10 =50cm2 10cm Rectangle 2 Area = l x b 4cm = 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 = = 156cm2

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**Volume of a Cylinder Volume = Area x height = πr2 = πr2h h x h**

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

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**Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm**

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

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**Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh**

The surface area of a cylinder is made up of 2 basic shapes can you name them. Cylinder (circular Prism) 2πr Curved Area =2πrh Top Area =πr2 Roll out curve side h Bottom Area =πr2 2 x Circles Rectangle Total Surface Area = 2πr2 + 2πrh

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**Surface Area of a Cylinder = (2 x π x 3²) + (2 x π x 3 x 10)**

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

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**Surface Area of a Cylinder = 2 x π x 3 x 9 = 169.64 cm2**

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 = cm2

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