Volume & Surface Area of Solids www.mathsrevision.com Revision of Area Revision of Volume and Surface Area Volume of a Prism Volume of a Cylinder www.mathsrevision.com Volume of a Pyramid Curved Area of a Cylinder Volume of a Sphere Exam Type Questions

Starter Questions a2 – 3b2 = 57 Q1. True or false Q2. Write down the probability of picking out a number greater than 20 in the national lottery. www.mathsrevision.com Q3. If a = -3 and b = -4 does a2 – 3b2 = 57 Q4. Calculate Tuesday, 11 April 2017 Created by Mr.Lafferty

Revision of Areas www.mathsrevision.com Any Type of Triangle Level 4 Any Type of Triangle Rhombus and kite www.mathsrevision.com Parallelogram Trapezium Circle

Compiled by Mr. Lafferty Maths Dept. Area Level 4 Learning Intention Success Criteria We are revising area of basic shapes. Know formulae. Use formulae correctly. www.mathsrevision.com Show working and appropriate units. 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Area Example : Find the area of the V – shape kite. Level 4 Example : Find the area of the V – shape kite. 4cm www.mathsrevision.com 7cm Tuesday, 11 April 2017 Created by Mr.Lafferty

Composite Areas We can use our knowledge of the basic areas Level 4 We can use our knowledge of the basic areas to work out more complicated shapes. Example : Find the area of the arrow. www.mathsrevision.com 5cm 3cm 6cm 4cm Tuesday, 11 April 2017 Created by Mr.Lafferty

Composite Areas 8cm www.mathsrevision.com 11cm 10cm Level 4 Example : Find the area of the shaded area. 8cm 11cm www.mathsrevision.com 4cm 10cm Tuesday, 11 April 2017 Created by Mr.Lafferty

Created by Mr. Lafferty Maths Dept. Composite Areas The Circle Level 4 Example : Find the area of the shape Area = rectangle + semicircle 20cm 5 cm www.mathsrevision.com 11-Apr-17 Created by Mr. Lafferty Maths Dept.

Area Now try TJ 4+ Ex 16.1 Ch16 (page 121) www.mathsrevision.com Level 4 Now try TJ 4+ Ex 16.1 Ch16 (page 121) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Q4. Rearrange into the form y = Starter Questions Q1. Find the area of the triangle. 10cm 3cm 4cm Q2. Expand out and simplify 2w2 – 3(2w – 5) www.mathsrevision.com Q3. True or false Q4. Rearrange into the form y = 2y – 3x + 7 = 0 Tuesday, 11 April 2017 Created by Mr.Lafferty

Compiled by Mr. Lafferty Maths Dept. Volume & Surface Area Level 4 Learning Intention Success Criteria We are revising volume and surface area of a cuboid. Know formulae. Use formulae correctly. www.mathsrevision.com Show working and appropriate units. 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid 3cm 4cm 6cm Level 4 18 cubes fit the base. www.mathsrevision.com = 1 centimetre cube = 1 cm³ 4 layers of 18 cubes = 4 x 18 = 72 centimetre cubes = 72 cm³ 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. A short cut ! 3cm 4cm 6cm Level 4 height Area of rectangle breadth www.mathsrevision.com length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example Working Volume = l x b x h Level 4 Heilander’s Porridge Oats V = 18 x 5 x 27 V = 2430 cm³ 27cm 5 cm 18 cm 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example Working Volume = l x b x h Level 4 V = 2 x 2 x 2 V = 8 cm³ www.mathsrevision.com 2cm 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example Find the volume of the composite shape. Level 4 VT = V1 + V2 7 cm 3 cm 5 cm VT = 105 + 720 10 cm 9 cm 8 cm VT = 825 cm3 V1 = l x b x h www.mathsrevision.com = 3 x 5 x 7 V2 = l x b x h = 105 cm³ = 8 x 10 x 9 = 720 cm³ 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Find the length the cuboid Example Find the length the cuboid This just an equation. We know how to solve them ! Level 4 4 cm Volume = L x B x H V=200cm3 200 = L x 5 x 4 5 cm www.mathsrevision.com 200 = 20L 10 cm L 20L = 200 L = 10 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example Liquid Volume Working Volume = l x b x h Level 4 V = 100 x 30 x 50 V = 150 000 cm³ 50 cm = 150 000 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. 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Face Edges and Vertices Don’t forget the faces edges and corners we can’t see at the back Face Edges and Vertices Level 4 The shape below is called a cuboid. It is made up of FACES, EDGES and VERTICES. Edges are where the two faces meet (lines) www.mathsrevision.com Faces are the sides of a shape (surface area) Vertices where lines meet (corners) 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Face Edges and Vertices Calculate the number of faces edges and vertices for a cuboid. Face Edges and Vertices Level 4 6 faces www.mathsrevision.com 12 edges Front and back are the same 8 vertices Top and bottom are the same Right and left are the same 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Face Edges and Vertices Calculate the number of faces edges and vertices for a cube. Face Edges and Vertices Level 4 6 faces www.mathsrevision.com 12 edges Faces are squares 8 vertices 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Find the surface area of the cuboid Example Find the surface area of the cuboid Working Level 4 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 www.mathsrevision.com 5cm Total Area = 20+20+15+15+12+12 = 94cm2 Front and back are the same Top and bottom are the same Right and left are the same 11-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Now try TJ 4+ Ex 16.2 Ch16 (page 122) Volume & Surface Area Level 4 Now try TJ 4+ Ex 16.2 Ch16 (page 122) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. True or false 2(x – 6) - 2(x + 6) = 0 Q2. Does 2.5 + 1.25 x 20 = 27.55 Explain your answer www.mathsrevision.com Q3. Factorise 2y2 + 3y +2 Q4. Calculate Tuesday, 11 April 2017 Created by Mr.Lafferty

Volume of Prisms www.mathsrevision.com Learning Intention Level 4 Learning Intention Success Criteria We are learning how to calculating volume of any prism given area. 1. Calculate the volume for various prisms. 2. Solution must include appropriate units and working. www.mathsrevision.com

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

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

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

Volume of Prisms Now try TJ 4+ Ex 16.3 Ch16 (page 124) Level 4 Now try TJ 4+ Ex 16.3 Ch16 (page 124) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. Find the area of the parallelogram Q2. Factorise 7 7 Q2. Factorise 4x + 40 www.mathsrevision.com Q3. A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4. The speed of light is 300000000 metres per sec. True or false in scientific notation 3 x 108. Tuesday, 11 April 2017 Created by Mr.Lafferty

Volume of a Cylinder www.mathsrevision.com Learning Intention Level 4 Learning Intention Success Criteria We are learning how to derive the formula for the volume of a cylinder and apply it to solve problems. To know formula. Apply formula correctly. www.mathsrevision.com Work backwards using formula.

Volume of a Cylinder Volume = Area x height = πr2 = πr2h Level 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 h www.mathsrevision.com = πr2 x h Cylinder (circular Prism) = πr2h

Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm3 = 784.5 cm3 Example : Find the volume of the cylinder below. 5cm Cylinder (circular Prism) 10cm V = πr2h www.mathsrevision.com = π(5)2x10 = 250π cm3 = 784.5 cm3

Volume of a Cylinder Now try TJ 4+ Ex 16.4 Ch16 (page 125) Level 4 Now try TJ 4+ Ex 16.4 Ch16 (page 125) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions -(a2) + b2 = 5 Q1. Factorise Q2. Write down the probability of picking out a number less than 30 in the national lottery. www.mathsrevision.com Q3. True or false if a = -1 and b = -2 -(a2) + b2 = 5 Q4. Explain why Tuesday, 11 April 2017 Created by Mr.Lafferty

Volume of a Pyramid www.mathsrevision.com Learning Intention Level 4 Learning Intention Success Criteria We are learning how to use the formula for the volume of ANY pyramid and apply it to solve problems. To know formula. Apply formula correctly. www.mathsrevision.com Work backwards using formula.

Volume of a Pyramid www.mathsrevision.com Level 4 cone The volume of any pyramid can be calculated using the formula www.mathsrevision.com A = Area of base h = height

Volume of Pyramid www.mathsrevision.com Level 4 Q. Find the volume the pyramid. 12m 100m2 www.mathsrevision.com

Volume of a Cone www.mathsrevision.com h r Level 4 h r www.mathsrevision.com If the above cone has radius 15cm and height of 10 cm. Calculate it’s volume.

Volume of a Pyramid Now try TJ 4+ Ex 16.5 Ch16 (page 127) Level 4 Now try TJ 4+ Ex 16.5 Ch16 (page 127) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. Expand out and simplify 3(x – 2) - ( - 3x + 4) Q2. Factorise 2x2 – 16x www.mathsrevision.com Q3. True or false Q4. By rearranging in y = , find the gradient and where the straight line crosses the x-axis y + 4x - 3 = 0 Tuesday, 11 April 2017 Created by Mr.Lafferty

Surface Area of a Cylinder www.mathsrevision.com Learning Intention Level 4 Learning Intention Success Criteria We are learning how to calculate the surface area of a cylinder by using basic areas. To know how to split up a cylinder. www.mathsrevision.com 2. Calculate the surface area of a cylinder.

Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh Level 4 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 www.mathsrevision.com Total Surface Area = 2πr2 + 2πrh

Surface Area of a Cylinder = 2π(3)2 + 2π x 3 x 10 = 18π + 60π Level 4 Example : Find the surface area of the cylinder below: 3cm Surface Area = 2πr2 + 2πrh 10cm = 2π(3)2 + 2π x 3 x 10 www.mathsrevision.com = 18π + 60π Cylinder (circular Prism) = 245 cm2

Surface Area of a Cylinder D = 25 25 D = π www.mathsrevision.com Diameter = 2r Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. D = 25 25 π 9cm 25cm www.mathsrevision.com D = = 7.96 cm Surface Area = 2πr2 + 2πrh = 2π(3.98) 2 + 2π(3.98)x9 = 99.5 + 225 = 324.5 cm2

Now try TJ 4+ Ex 16.6 Ch16 (page 129) Surface Area of a Cylinder Level 4 Now try TJ 4+ Ex 16.6 Ch16 (page 129) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Starter Questions Q1. Find the area of the triangle. 10cm Q2. Factorise 4x2 – 64x 6cm www.mathsrevision.com Q3. Calculate Q4. Rearrange equation in y = y – 2x + 5 = 0 Tuesday, 11 April 2017 Created by Mr.Lafferty

Volume of Solids www.mathsrevision.com Learning Intention Level 4 Learning Intention Success Criteria We are learning how to use the sphere formula and use it to solve real-life problems. To know the volume formula for a sphere. Work out volumes for spheres. www.mathsrevision.com Answer to contain appropriate units and working.

Volume of a Sphere www.mathsrevision.com D = diameter r Level 4 D = diameter r D www.mathsrevision.com Q. If the above sphere has radius 10cm. Calculate it’s volume.

Volume of a sphere Q. Find the volume the composite shape. Level 4 Q. Find the volume the composite shape. Volume = Cylinder + half a sphere ½ sphere Cylinder www.mathsrevision.com r 2m h = 6m

Now try TJ 4+ Ex 16.7 Ch16 (page 130) Volume of a sphere Level 4 Now try TJ 4+ Ex 16.7 Ch16 (page 130) www.mathsrevision.com Tuesday, 11 April 2017 Created by Mr. Lafferty @www.mathsrevision.com

Part b on next slide