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

The top of the Mallow puff is a half sphere. Radius - 2.13cm Formula for sphere -

V = (4÷3) x π x 2.13 x 2.13 x 2.13

V = 38.71 but ÷ 2 to get half a sphere volume

V = 19.40cm3

Just the Marshmellow

The top of the Mallow puff is a half sphere. Radius - 2cm Formula for sphere -

V = (4÷3) x π x 2 x 2 x 2

V = 33.51 but ÷ 2 to get half a sphere volume

V = 16.76cm3 TOTAL amount of chocolate on the top of the Mallow- Puff

19.40 - 16.76 = 2.64cm3 (Choc + Marshmellow) - (Marshmellow) = Just Chocolate

The bottom of the Mallow puff is a cylinder. Radius - 2.5cm Height - 0.8cm Formula for cylinder -

The MallowPuff

Bottom half

Chocolate + Biscuit

Just the Biscuit

The bottom of the Mallow puff is a cylinder. Radius - 2.2cm Height - 0.7cm 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

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 the Lindt ball 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

Total value

Bottom half

The bottom half of the Toblerone is a trapezium. Height - 1cm Length - 20.6cm A - 2cm B - 3cm

Toblerone

A + B ÷ 2 2 + 3 ÷ 2 = 2.5

V = 2.5 x 20.6 x 1 V = 51.5cm3

Amount of chocolate on the base of the Toblerone = 51.5cm3

Top half

The top half of the Toblerone is a trapezium. Height - 1.8cm Length - 1.1cm A - 0.2cm B - 2cm

Toblerone

A + B ÷ 2 0.2 + 2 ÷ 2 = 1.1

V = 1.1 x 1.8 x 1.1 V = 2.18cm3

Amount of chocolate on the top of the Toblerone = 26.16cm3

2.18 x 12 because there is twelve trapeziums on top of the base

2.18 x 12 = 26.16

Total value

Toblerone

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

The shape of the milo tin is a cylinder. Radius - 7.75cm Height - 23cm Formula for cylinder -

TOTAL amount of chocolate in the milo tin

Total value

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 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

Total value

Wittaker's Chocolate Bar Total value

The shape of the wittakers chocolate bar is a trapezium. Height - 1.3cm Length - 20cm A - 10cm B - 11cm A + B ÷ 2 = 10 + 11 = 21 ÷ 2 = 10.5

V = 10.5 x 1.3 x 20 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 crate a circle. Radius - 1.3cm Height - 0.1cm Formula for the area of the circle -

A = π x 1.3 x 1.3 A = 5.31cm2

The middle bit between the two half circles is a rectangle. Width - 3.4cm Length - 4cm Formula for the area of the rectangle -

A = 3.4 x 4 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

• ne costs more.

The milo tin wrapping goes around the tin but does not cover the bottom or the top, and there is a 10mm overlap. This wrapping costs 1cent per square centimetre.

The Milo Tin

If we peel the wrapping off the tin it would be a rectangle with these measurements: Length - 48.9cm + 1cm = 49.9 Width - 22.3cm Area of a rectangle formula - A = 49.9 x 22.3 A = 1112.77cm2 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 wrapping of the pyramid covers the four sides which can be measured as triangles and then the base

• f the pyramid needs to be measured as a square.

This wrapping costs 3cent per square centimetre.

The pyramid

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

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 Area of a square formula - side2

A = 10 x 10 A = 100

The area of the base / square wrapping is 100cm2

A = (5 x 11)÷ 2 A = 55cm2

The wrapping of the pyramid covers the four sides which can be measured as triangles and then the base

• f the pyramid needs to be measured as a square.

This wrapping costs 3cent per square centimetre.

The pyramid

TOTAL area of pyramid 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.

The 4 sides + the base square = total amount of wrapping

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. Height - 10cm Width - 8cm Length- 20cm The chocolate on a single Mallow-puff: 7.71cm3 The chocolate on 1 million Mallow-puffs: 7.71 x 1000000 = 7,710,000 The chocolate in the block V = 20 x 8 x 10 V = 1600cm3 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.

Radius - 11.8 Height - 44.5

V = π x 11.8 x 11.8 x 44.5 V = 19465.87cm3

The marshmallow in a single Mallow-puff:

V = 16.76cm3

The marshmallow in a million Mallow-puffs:

V = 16.76 x 1000000 = 16,760,000

The amount of marshmallow in the Container 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 Mallow-puff:

V = 10.64cm3

The marshmallow in a million Mallow-puffs:

V = 10.64 x 1000000 = 10,640,000

A - 11.8cm B - 44.5cm Height - 17cm Length - 17cm

The amount of biscuit in the Container

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