S4_General_Volume_TJ_Chapter8

# S4_General_Volume_TJ_Chapter8 - Volume S4...

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Unformatted text preview: Volume S4 www.mathsrevision.com Counting Volume cubes Volume of a cuboid Liquid Volumes Volume of cylinder Volume of triangular prism 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 Learning Intention Success Criteria 1. To know what volume means. 2. Work out volumes using 1cm cubes. 3. Answer to contain appropriate units. 3 www.mathsrevision.com 1. To understand the term volume in terms of counting cubes. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 Volume is the amount of space a 3D - shape takes up www.mathsrevision.com 1cm 1cm 1c m One Unit of Volume is the "CUBIC CENTIMETRE" = 1 centimetre cube 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. = 1 cm Volumes by Counting Cubes S4 This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm? www.mathsrevision.com 1cm cm 1 1cm 1cm = 2 centimetre cubes 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. = 2 cm Volumes by Counting Cubes S4 This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm www.mathsrevision.com 1cm 1cm 1cm cm 1 = 3 centimetre cubes 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. = 3 cm Volumes by Counting Cubes S4 What is its volume in cm of these shapes. www.mathsrevision.com 5 cm 5 cm 13 Feb 2012 3 3 6 cm 3 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 One unit of Volume is the "CUBIC CENTIMETRE" www.mathsrevision.com 3cm cm 2 4cm Volume = 24 centimetre cube = 24 cm Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Volumes by Counting Cubes S4 www.mathsrevision.com Now try Ex 1 Ch8 (page 89) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions S4 www.mathsrevision.com Student Discount off the price of each pizza 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid S4 Learning Intention Success Criteria 1. To know the formula. 2. Use formula correctly. 3. Show working and appropriate units. www.mathsrevision.com 1. To understand how to calculate the volume of cuboid. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid S4 www.mathsrevision.com 4cm 3cm 18 cubes fit the base. 6cm = 1 centimetre cube = 1 cm 4 layers of 18 cubes = 4 x 18 13 Feb 2012 = 72 centimetre cubes Compiled by Mr. Lafferty Maths Dept. = 72 cm A short cut ! S4 www.mathsrevision.com height 4cm 3cm Area of rectangle length 6cm breadth Volume = 6 x 3 x 4 = 72 cm Volume = length x breadth x height 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Example 1 S4 Working Volume = l x b x h V = 18 x 5 x 27 V = 2430 cm 27cm 5 c m Heilander's Porridge Oats 18 cm 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Example 2 Working S4 Volume = l x b x h V = 2 x 2 x 2 V = 8 cm www.mathsrevision.com 2cm 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid S4 www.mathsrevision.com Now try Ex 2 Ch8 (page 92) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Question S4 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 Learning Intention Success Criteria 1. To know the term liquid volume. 2. Work out volumes using 1ml and litres. 3. Answer to contain appropriate units. www.mathsrevision.com 1. To understand the term liquid volume using millilitres and litres. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 How much water does this hold? 1 cm I'm a very small duck! 1 cm 1 cm Volume = 13 Feb 2012 l x b x h = 1 cm Compiled by Mr. Lafferty Maths Dept. A cube with volume 1cm holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre. Example 1 Liquid Volume S4 Working Volume = l x b x h V = 6 x 3 x 12 V = 216 cm = 216 ml So the carton can hold 216 ml of orange juice. Remember: 1 cm = 1 ml www.mathsrevision.com 12 cm 3 c m Orange Flavour 6 cm How much juice can this carton hold? 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Example 2 Liquid Volume S4 Working Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm 30 cm 50 cm 100 cm = 150 000 ml = 150 litres 3 So the fish tank can hold 150 1cm = 1 ml litres of water. 1000 ml = 1 litre How much water can this fish tank hold in litres? 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 www.mathsrevision.com Now try Ex 3 Ch8 (page 94) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions Q1. www.mathsrevision.com Q2. Q3. Find the area of the triangle. Factorise 4x 64 Calculate 10cm 6cm 4 0 1.6 5 5 0 Monday 13 February 2012 Created by Mr.Lafferty 23 Volume of a Cylinder Learning Intention Success Criteria 1. To know formula. 2. Apply formula correctly. www.mathsrevision.com 1. To derive the formula for the volume of a cylinder and apply it to solve problems. 3. Work backwards using formula. Volume of a Cylinder The volume of a cylinder can be thought as being a pile of circles laid on top of each other. www.mathsrevision.com Volume = Area x height = r2 x h = r2h h Cylinder (circular Prism) Volume of a Cylinder Example : Find the volume of the cylinder below. www.mathsrevision.com 5cm V = r2h = (5)2x10 = 250 cm Cylinder (circular Prism) 10cm Volume of Solids www.mathsrevision.com Now try Extension Booklet Starter Questions Q1. 35% of 360 Q2. Calculate 5 + 6 x 7 Q3. Expand 2( y 5 ) www.mathsrevision.com Monday 13 February 2012 Created by Mr.Lafferty 28 Volume of Solids Prisms Learning Intention Success Criteria 1. To know the volume formula for any prism. 2. Work out volumes for various prisms. 3. Answer to contain appropriate units and working. www.mathsrevision.com 1. To understand the prism formula for calculating volume. Volume of Solids Definition : A prism is a solid shape with uniform crosssection www.mathsrevision.com Hexagonal Prism Cylinder (circular Prism) Triangular Prism Pentagonal Prism Volume = Area of Cross section x length Any Triangle Area www.mathsrevision.com h = vertical height Sometimes called the altitude b h 1 Ar e a = b 2 Created by Mr.Lafferty h 31 Monday 13 February 2012 Any Triangle Area Example 1 : Find the area of the triangle. www.mathsrevision.com 6cm 8cm 1 Ar e a = b 2 h 1 Ar e a = 8 6 2 Ar e a = 2 4c m 2 Monday 13 February 2012 Created by Mr.Lafferty 32 Volume of Solids Definition : A prism is a solid shape with uniform crosssection Q. Find the volume the triangular prism. Triangular Prism www.mathsrevision.com Volume = Area x length = 20 x 10 = 200 cm 3 10cm 20cm 2 Volume of a Triangular Working Prism Triangle Area = 1 bh 2 2 = 2 x4 = 8 cm www.mathsrevision.com 4cm 10cm 4cm Volume = Area x length 3 = 8 x 10 = 80cm 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Example Find the volume of the triangular prism. Working Triangle Area = 1 bh 2 2 = 3 x 3 = 9 cm www.mathsrevision.com 3cm 6cm 30cm Volume = Area x length 3 = 9 x 30 = 270cm Total Area 2 = 6+6+30+40+50 = 132cm Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Volume of Solids www.mathsrevision.com Now try Extension Booklet ...
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