Volume www mathsrevision com National 4 Counting Volume

Volume www. mathsrevision. com National 4 Counting Volume cubes Volume of a cuboid Liquid Volumes Volume of cylinder Volume of triangular prism 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes www. mathsrevision. com National 4 Learning Intention 1. To understand the term volume in terms of counting cubes. Success Criteria 1. To know what volume means. 2. Work out volumes using 3 1 cm cubes. 3. Answer to contain appropriate units. 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes National 4 m 1 cm 1 c www. mathsrevision. com Volume is the amount of space a 3 D - shape takes up One Unit of Volume is the “CUBIC CENTIMETRE” = 1 centimetre cube = 1 cm³ 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³? m 1 cm 1 c www. mathsrevision. com National 4 = 2 centimetre cubes = 2 cm³ 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³ m 1 cm 1 c www. mathsrevision. com National 4 1 cm = 3 centimetre cubes = 3 cm³ 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes National 4 www. mathsrevision. com What is its volume in cm³ of these shapes. 5 cm 02 -Nov-20 3 6 cm 3 Compiled by Mr. Lafferty Maths Dept. 3

Volumes by Counting Cubes National 4 m 3 cm 4 cm 2 c www. mathsrevision. com One unit of Volume is the “CUBIC CENTIMETRE” Volume = 24 centimetre cube = 24 cm³ 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volumes by Counting Cubes www. mathsrevision. com National 4 Now try Ex 1 Ch 8 (page 89) 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

National 4 Starter Questions www. mathsrevision. com National 4 Student Discount ⅓ off the price of each pizza 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volume of a cuboid www. mathsrevision. com National 4 Learning Intention 1. To understand how to calculate the volume of cuboid. Success Criteria 1. To know the formula. 2. Use formula correctly. 3. Show working and appropriate units. 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volume of a cuboid www. mathsrevision. com National 4 18 cubes fit the base. 4 cm 6 cm 3 cm = 1 centimetre cube = 1 cm³ 4 layers of 18 cubes = 4 x 18 = 72 centimetre cubes = 72 cm³ 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

A short cut ! www. mathsrevision. com National 4 height Area of rectangle 4 cm 6 cm 3 cm breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Example 1 Working Volume = l x b x h National 4 V = 18 x 5 x 27 V = 2430 cm³ 27 cm 5 Heilander’s cm Porridge Oats 18 cm 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Example 2 Volume = l x b x h National 4 www. mathsrevision. com Working V=2 x 2 x 2 V = 8 cm³ 2 cm 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Example 3 Find the volume of the composite shape. www. mathsrevision. com National 4 5 cm VT = V 1 + V 2 7 cm 3 cm VT = 105 + 720 9 cm V 1 = l x b x h =3 x 5 x 7 = 105 cm³ 10 cm 8 cm 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept. VT = 825 cm 3 V 2 = l x b x h = 8 x 10 x 9 = 720 cm³

www. mathsrevision. com National 4 Example 4 Find the length the cuboid 4 cm V=200 cm 3 This just an equation. We know how to solve them ! Volume = L x B x H 5 cm 200 = L x 5 x 4 200 = 20 L 10 L cm 20 L = 200 L = 10 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Volume of a cuboid www. mathsrevision. com National 4 Now try Ex 2 Ch 8 (page 92) 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Liquid Volume www. mathsrevision. com National 4 Learning Intention 1. To understand the term liquid volume using millilitres and litres. Success Criteria 1. To know the term liquid volume. 2. Work out volumes using 1 ml and litres. 3. Answer to contain appropriate units. 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Liquid Volume I’m a very small duck! How much water does this hold? National 4 1 cm Volume = l x b x h = 1 cm³ A cube with volume 1 cm³ holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre. 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Example 1 Liquid Volume Working Volume = l x b x h National 4 www. mathsrevision. com V = 6 x 3 x 12 12 cm 3 cm = 216 ml Orange Flavour 6 cm How much juice can this carton hold? 02 -Nov-20 V = 216 cm³ So the carton can hold 216 ml of orange juice. Remember: 1 cm³ = 1 ml Compiled by Mr. Lafferty Maths Dept.

Example 2 Liquid Volume National 4 Working Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³ 30 50 cm cm = 150 000 ml = 150 litres 100 cm How much water can this fish tank hold in litres? 02 -Nov-20 3 tank can So the fish 1 cm = 1 ml hold 150 ml litres of water. 1000 = 1 litre Compiled by Mr. Lafferty Maths Dept.

Liquid Volume www. mathsrevision. com National 4 Now try Ex 3 Ch 8 (page 94) 02 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 Q 1. Find the area of the triangle. Q 2. Factorise 4 x - 64 Q 3. Calculate Monday, November 2, 2020 Created by Mr. Lafferty 10 cm 6 cm 25

Volume of a Cylinder www. mathsrevision. com National 4 Learning Intention 1. To derive the formula for the volume of a cylinder and apply it to solve problems. Success Criteria 1. To know formula. 2. Apply formula correctly. 3. Work backwards using formula.

Volume of a Cylinder www. mathsrevision. com National 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 = πr 2 x h = πr 2 h h Cylinder (circular Prism)

Volume of a Cylinder National 4 www. mathsrevision. com Example : Find the volume of the cylinder below. 5 cm V = πr 2 h = π(5)2 x 10 = 250π cm 10 cm Cylinder (circular Prism)

Volume of Solids www. mathsrevision. com National 4 Now try Extension Booklet

Starter Questions www. mathsrevision. com National 4 Q 1. 35% of 360 Q 2. Calculate 5 + 6 x 7 Q 3. Expand 2( y – 5 ) Monday, November 2, 2020 Created by Mr. Lafferty 30

Volume of Solids Prisms www. mathsrevision. com National 4 Learning Intention 1. To understand the prism formula for calculating volume. 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.

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

Any Triangle Area www. mathsrevision. com National 4 Monday, November 2, 2020 h = vertical height Sometimes called the altitude h b Created by Mr. Lafferty 33

Any Triangle Area National 4 www. mathsrevision. com Example 1 : Find the area of the triangle. Monday, November 2, 2020 6 cm 8 cm Created by Mr. Lafferty 34

Volume of Solids www. mathsrevision. com National 4 Definition : A prism is a solid shape with uniform cross-section Q. Find the volume the triangular prism. Triangular Prism Volume = Area x length = 20 x 10 = 200 cm 3 10 cm 2

Volume of a Triangular Prism Working Triangle Area = www. mathsrevision. com National 4 = 2 x 4 = 8 cm Volume = Area x length 3 = 8 x 10 = 80 cm 4 cm 02 -Nov-20 2 10 cm 4 cm Created by Mr. Lafferty Maths Dept.

Example www. mathsrevision. com National 4 Find the volume of the triangular prism. Working Triangle Area = = 3 x 3 = 9 cm 3 cm 02 -Nov-20 30 cm 2 Volume = Area x length 3 = 9 x 30 = 270 cm 6 cm Total Area 2 = 6+6+30+40+50 = 132 cm Compiled by Mr. Lafferty Maths Dept.

Volume of Solids www. mathsrevision. com National 4 Now try Extension Booklet