Assessment By Hannah Clayton What we have to measure Exercise 1 - PowerPoint PPT Presentation

Willy Walton Assessment By Hannah Clayton

What we have to measure

Exercise 1 To measure different types of chocolate and find the chocolate with the greatest volume.

The MallowPuff Top half Chocolate + Marshmellow Just the Marshmellow The top of the Mallow puff is a half sphere. The top of the Mallow puff is a half sphere. Radius - 2.13cm Radius - 2cm Formula for sphere - Formula for sphere - V = (4÷3) x π x 2.13 x 2.13 x 2.13 V = (4÷3) x π x 2 x 2 x 2 V = 38.71 but ÷ 2 to get half a sphere V = 33.51 but ÷ 2 to get half a sphere volume volume V = 19.40cm3 V = 16.76cm3 TOTAL amount of chocolate on the top of the Mallow- Puff (Choc + Marshmellow) - (Marshmellow) = Just Chocolate 19.40 - 16.76 = 2.64cm3

The MallowPuff Bottom half Chocolate + Biscuit Just the Biscuit The bottom of the Mallow puff is a The bottom of the Mallow puff is a cylinder. cylinder. Radius - 2.5cm Radius - 2.2cm Height - 0.8cm Height - 0.7cm Formula for cylinder - Formula for sphere - V = π x 2.5 x 2.5 x 0.8 V = π x 2.2 x 2.2 x 0.7 V = 15.71cm3 V = 10.64cm3 TOTAL amount of chocolate on the bottom of the Mallow-Puff (Choc + biscuit) - (biscuit) = Just Chocolate 15.71 - 10.64 = 5.07cm3

The MallowPuff Total value TOTAL amount of chocolate on the whole of the Mallow-Puff Base + Top = total value of chocolate 5.07 + 2.64 = 7.71cm3 TOTAL amount of chocolate in 1000 Mallowpuffs Chocolate on 1 MallowPuff x 1000 = total value of chocolate 7.71 x 1000= 7710cm3 TOTAL amount of chocolate 1000 Mallowpuffs = 7710cm3

Lindt ball chocolates Total value TOTAL amount of chocolate in the Lindt ball The shape of the Lindt chocolate is a sphere. Radius - 1.4 Formula for sphere - V = (4÷3) x π x 1.4 x 1.4 x 1.4 V = 11.49cm3 TOTAL amount of chocolate in 100 Lindt balls Chocolate on 1 Lindt ball x 100 = total value of chocolate 11.49 x 100= 1149cm3 TOTAL amount of chocolate in 100 Lindt balls = 1149cm3

Toblerone Bottom half Amount of chocolate on the base of the Toblerone = 51.5cm3 The bottom half of the Toblerone is a trapezium. Height - 1cm Length - 20.6cm A + B ÷ 2 A - 2cm 2 + 3 ÷ 2 = 2.5 B - 3cm V = 2.5 x 20.6 x 1 V = 51.5cm3

Toblerone Top half Amount of chocolate on the top of the Toblerone = 26.16cm3 The top half of the Toblerone is a trapezium. Height - 1.8cm A + B ÷ 2 Length - 1.1cm 0.2 + 2 ÷ 2 = 1.1 A - 0.2cm V = 1.1 x 1.8 x 1.1 B - 2cm V = 2.18cm3 2.18 x 12 because there is twelve 2.18 x 12 = 26.16 trapeziums on top of the base

Toblerone Total value TOTAL amount of chocolate on the whole of the medium sized Toblerone Base + Top = total value of chocolate 51.5 + 26.16 = 77.66cm3 TOTAL amount of chocolate in 40 Toblerones Chocolate on 1 Toblerone x 40 = total value of chocolate 77.66 x 40= 3106.4cm3 TOTAL amount of chocolate in 40 Toblerones = 3106.4cm3

Milo Tin Total value TOTAL amount of chocolate in the milo tin The shape of the milo tin is a cylinder. Radius - 7.75cm Height - 23cm Formula for cylinder - V = π x 7.75 x 7.75 x 23 V = 4339.91cm3 TOTAL amount of chocolate in 1 milo tin = 4339.91cm3

Chocolate Pyramid Total value TOTAL amount of chocolate in the chocolate pyramid The shape of the chocolate pyramid is a pyramid. Base width - 10cm Base length - 10cm Height - 9.7cm Formula for pyramid - V = (10 x 10 x 9.7) ÷ 3 V = 323.33cm3 TOTAL amount of chocolate in 1 chocolate pyramid = 323.33cm3

Wittaker's Chocolate Bar Total value The shape of the wittakers chocolate bar is a trapezium. Height - 1.3cm Length - 20cm A + B ÷ 2 = 10 + 11 = 21 ÷ 2 = 10.5 A - 10cm V = 10.5 x 1.3 x 20 B - 11cm V = 273cm3 TOTAL amount of chocolate in 15 Wittaker's chocolate bars Chocolate on 1 chocolate bar x 15 = total value of chocolate 273 x 15= 4095cm3 TOTAL amount of chocolate in 15 chocolate bars = 4095cm3

Chocolate Thins The two ends of the biscuit joint together The middle bit between the two half crate a circle. circles is a rectangle. Radius - 1.3cm Width - 3.4cm Height - 0.1cm Length - 4cm Formula for the area of the circle - Formula for the area of the rectangle - A = π x 1.3 x 1.3 A = 3.4 x 4 A = 5.31cm2 A = 13.6cm2 TOTAL amount of chocolate in the chocolate thins To get the full volume of chocolate you have to add the area of the circle and then the area of the rectangle and then times the outcome by 0.1 (height of the chocolate) 5.31 + 13.6 = 18.91 18.91 x 0.1 = 1.891cm3

Which chocolate has the greatest amount of chocolate? • 1000 Mallow-puffs = 7710cm3 • 2000 Chocolate thins = 3782cm3 • 40 medium Toblerones = 3016.4cm3 • 1 large Milo tin filled with chocolate = 4339.91cm3 • 1 pyramid chocolate = 323.33cm3 • 15 large Wittakers bars = 4095cm3 • 100 Lindt ball chocolates = 1149cm3 Mallow puffs have the largest volume of chocolate.

Exercise 2 To measure the wrapping and which one costs more.

The Milo The milo tin wrapping goes around the tin but does not cover the bottom or the top, and there is a Tin 10mm overlap. This wrapping costs 1cent per square centimetre. If we peel the wrapping off the tin it would be a rectangle with these measurements: A = 49.9 x 22.3 Length - 48.9cm + 1cm = 49.9 A = 1112.77cm2 Width - 22.3cm Area of a rectangle formula - The area of the milo tin wrapping is 1112.77cm2 TOTAL cost of milo tin wrapping Area of wrapping x cost (0.01) = total cost of wrapping 1112.77 x 0.01= $11.13 Answer rounded to 2dp

The The wrapping of the pyramid covers the four sides which can be measured as triangles and then the base pyramid of the pyramid needs to be measured as a square. This wrapping costs 3cent per square centimetre. Is we get the area for a triangle with these measurements and then times by 4 we will get the wrapping for all the 4 sides: Height - 11cm Base - 10cm Area of a triangle formula = 1/2 base x height A = (5 x 11)÷ 2 A = 55cm2 The area of the triangle wrapping is 55cm2. 55 x 4 = 220cm2 Then to get the base we have to find the area of a square: Side - 10cm A = 10 x 10 Area of a square formula - side2 A = 100 The area of the base / square wrapping is 100cm2

The The wrapping of the pyramid covers the four sides which can be measured as triangles and then the base pyramid of the pyramid needs to be measured as a square. This wrapping costs 3cent per square centimetre. TOTAL area of pyramid wrapping The 4 sides + the base square = total amount of wrapping Area of wrapping = 220 + 100= 320cm2 TOTAL cost of pyramid wrapping Area of wrapping x cost (0.03) = total cost of wrapping 320 x 0.03= $9.60 The milo tin wrapping costs more than the pyramid wrapping. The milo tin wrapping costs $1.53 more to wrap.

Exercise 3 To measure all parts of the mallow puff and work out how much chocolate, biscuit, and marshmallow would be needed to make 1 million mellow-puffs.

The chocolate The chocolate blocks are imported in rectangles and costs $6.99 each. The chocolate on a Height - 10cm single Mallow-puff: Width - 8cm 7.71cm3 Length- 20cm The chocolate on 1 million Mallow-puffs: The chocolate in the block V = 20 x 8 x 10 7.71 x 1000000 = V = 1600cm3 7,710,000 7,710,000 ÷ 1600 = 4818.75 4819 rectangle blocks of chocolate would be needed to make 1 million MallowPuffs / Choccy Wonkas

The marshmallow The marshmallow containers are imported in cylinders and costs $8.46 each. The marshmallow in a Radius - 11.8 single Mallow-puff: Height - 44.5 V = 16.76cm3 The marshmallow in a The amount of marshmallow in million Mallow-puffs: the Container V = 16.76 x 1000000 = V = π x 11.8 x 11.8 x 44.5 16,760,000 V = 19465.87cm3 16,760,000 ÷ 19,465.87 = 860.99414 861 cylinder blocks of marshmallow would be needed to make 1 million MallowPuffs / Choccy Wonkas

The biscuit The biscuit containers are imported in trapeziums and cost $12.33 each. The biscuit in a single A - 11.8cm Mallow-puff: B - 44.5cm V = 10.64cm3 Height - 17cm The marshmallow in a Length - 17cm million Mallow-puffs: The amount of biscuit in the Container V = 10.64 x 1000000 = 10,640,000 V = 1/2 (25 + 20) x 17 x 17 V = 6502.5cm3 10,640,000 ÷ 6502.5 = 1636.29cm3 1637 cylinder blocks of marshmallow would be needed to make 1 million MallowPuffs / Choccy Wonkas

How much it costs The labour is 8c for each MallowPuff made, so for 1 million MallowPuffs: 0.08 x 1000000 = $80,000 The chocolate blocks cost $6.99 each and there are 4819 needed to make 1 million MallowPuffs: 6.99 x 4819 = $33,684.81 The marshmallow tins cost $8.46 each and there are 861 needed to make 1 million MallowPuffs: 861 x 8.46 = $7284.06 The biscuit containers cost $12.33 each and there are 1637 needed to make 1 million MallowPuffs: 12.33 x 1637 = $20,184.21

Total cost of making 1000000 MallowPuffs 80,000 + 33,648.81 + 7284.06 + 20,184.21 = $141117.08 The total cost to make 1 million MallowPuffs / Choccy Wonkas is $141117.08