Basic Measuring and Calculations

Formulas, Workings Hints and Tips

When working out mathematics

• Start by writing down the formula • Ensure you show all working out (Marks will

be awarded for working out) • Substitute the appropriate figures into the

formula • Apply the appropriate formulas to each part of

the equation

What are types of measuring tools?

• Four fold rule – ideal for measurements up to 1 metre in length

• Retractable metal tape - suitable for measurements from 1 metre to 10 metres

• Fibreglass tape - used for long measurements e.g. building setout

• Scale rule – used for scaling dimensions off plans

Unit Conversion

• When working out the quantity of materials all measurements must be in the same units e.g. metres NOTE : (As a general rule if a question is printed in millimetres it is often easier to convert it to metres at the beginning of the equation unless the question asks for it to be answered in metres)

• To convert units for e.g. 1.000 metres to millimetres x by 1000 = 1000 millimetres

• To convert from millimetres to metres e.g. 1000 millimetres ÷ 1000 = 1.000 metres

• For more information refer to page 151 of your text book table 5.1

What units of measurement are used in the building industry?

• Linear measurements – e.g. measuring a piece

of timber • Linear measurements – are in millimetres and

metres • Refer to page 151 of the text book for units of

measurement used in the building industry

How are materials measured (Lineal measurement) ?

• Linear measurements are measured in mm or metres e.g. measuring the length of a wall is measured in lineal metres

Brick wall

3.000 metres

• Therefore the lineal length of the brick wall is 3.000 metres long

How are materials measured (Lineal measurement) ?

• Linear measurements are measured in mm or metres e.g. measuring the length of each wall around a room and adding those measurements together

5.000 metres

2.00

0 m

etre

s

•The total length around the room = 5.0 + 2.0 + 5.0 + 2.0 = 14 lineal metres •Formula = P1 + P2 + P3 + P4 = Total lineal metres

How are materials measured (Lineal) ?

• Circumference of a circle is the metre length around a circular object e.g. The tape measure length around the rim of a water tank

Water tank

•Circumference of a circle = 2 x pi x r

•Circumference = 2 x 3.14 x 1.5

• Circumference = 9.42 metres

NOTE : The answer is measured in metres only because there is only one measurement in the equation

Radius 1.5 m

Area Formulas

How are materials measured (Area) ?

• Area is measured in mm ² or metres ² • Formula for area of a rectangle Area = Length

x Width (The answer is always followed by the ² symbol)

Swimming pool cover

6.0 metres

2.0

met

res

• Area = L x W

• Area = 6.0 x 2.0

• Area = 12.0 metres² Note : The answer is in metres² because there are two measurements in the equation

How are materials measured (Odd Shapes Area) ?

• Area is measured in mm ² or metres ² • Formula for area of a rectangle Area = Length

x Width

• Area A = L x W

• Area A = 5.0 x 2.0

• Area A = 10.0 metres² Area A

Area B

5.0 metres 2.

0 m

etre

s

2.0

met

res

3.0 metres

• Area B = L x W • Area B = 3.0 x 2.0 • Area B = 6.0 metres²

Total Area A + B = 10.0 + 6.0 =16 m²

How are materials measured (Area) ?

• Area is measured in mm ² or metres ² • Formula for area of a circle Area = Pie x R² • (The answer is always followed by the ² symbol for area)

• Area = Pie x R²

• Area = 3.14 x 2.0²

• Area = 12.57 metres² Note : The answer is in metres² because there are two measurements in the equation (Pie & Radius)

Diam

eter 4.0 m

Radius 2.0 m

Cover for circular swimming pool

How are materials measured (Area) ?

• Area is measured in mm ² or metres ² • Formula for area of a triangle Area = ½ x Base

x Height (The answer is always followed by the ² symbol)

• Area = ½ x Base x Height

• Area = ½ x 4.0 x 3.0

• Area = 6.0 metres² Note : The answer is in metres² because there are two measurements in the equation

4.0 metres

3.0

met

res

Cover for triangle shaped swimming pool

How are materials measured (Area) ? • Area is measured in mm ² or metres ² • Formula for area of an irregular shape • Area =( length A + length B) x Height • (The answer is always followed by the ² symbol for area)

• Area = (length A + length B) x Height

• Area = (3.0 + 2.0) x 1.5

• Area = 4.0 metres²

Note : The answer is in metres² because there are two measurements in the equation

3.0 metres

2.0 metres

1.5

met

res

2

2

2

Cover for irregular shaped swimming

pool

How are materials measured (Rectangle Volume) ?

• Volume is measured in mm ³ or metres ³ Formula for Volume = Length x Width x Depth

(The answer is always followed by the ³ symbol)

1.5

m

Volume = L x W x D Volume = 6.0 x 2.0 x 1.5 Volume = 18.0 metres³ Note : The answer is in metres³ because there are three measurements in the equation

Amount of water in the swimming pool

How are materials measured (Cylinder Volume) ?

• Volume is measured in mm ³ or metres ³ Formula for Volume = Pie x R² x Height (The

answer is always followed by the ³ symbol)

Volume = Pie x R² x Height Volume = 3.41 x 1.0 x 3.0 Volume = 9.42 metres³ Note : The answer is in metres³ because there are three measurements in the equation

3.0

met

res

1. 0 m radius

Amount of water in water tank

tank

How are materials measured (Triangular Prism Volume) ?

• Volume is measured in mm ³ or metres ³ • Volume = (½ x base x Height) x Length (The answer is always followed by the ³ symbol)

Volume = (½ x base x Height) x Length Volume = (½ x 3.0 x 2.0) x 5.0 Volume = 15.0 metres³ Note : The answer is in metres³ because there are three measurements in the equation

3.0 metres

2.0

met

res

Amount of oxygen inside the tent

How are materials measured (Odd Shapes Volume) ?

• Calculate the lineal length of concrete footings required & how much concrete is needed in metres³

Length = footing length – footing width

•Side 1 = 5.0 – 0.600 = 4.4m

•Side 2 = 2.0 – 0.600 = 1.4m

•Side 3 = 2.0 – 0 = 2.0m

•Side 4 = 2.0 – 0 = 2.0m

•Side 5 = 3.0 – 0.600 = 2.4m

•Side 6 = 4.0 – 0.600 = 3.4m= 15.6Lin/M

Volume = Lineal length x width x depth

5.0 metres 2.

0 m

etre

s

2.0

met

res

3.0 metres Volume = 15.6 x 0.600 x 0.400 = 3.74m³

0.600 m wide footing

4.0

met

res

NOTE : Footing depth 0.400 m x 0.600 wide

Stud quantity key points

When working out how many timber studs are in a timber frame wall:

• Divide the length of the wall by the stud spacing

• Round up the answer e.g. 7.2 say 8 • Then add 1 therefore 8 becomes 9 • Refer to page 164 of text book for an example

How are materials measured (Quantity or Number of Studs) ?

No. of studs (length of wall) + 1 (Extra stud) Stud spacing No. of studs (8.0metres) = 13.33 say 14 +1 = 15 studs 0.600 m

8.0 metres

Tim

ber s

tud

wal

l

Wall plates quantity key points When working out how many top and bottom

plates for a timber wall frame: • Divide the length of the wall by the length of

timber you are using • Multiply the answer by 2 because there is a top

plate & a bottom plate • Then round up the answer at the end of the

calculation • E.g. 7.4 lengths of timber becomes 8/6.0

How are materials measured (Quantity or Number of Plates) ?

No. of Top or Bottom plates = (length of wall) x 2 Available Timber length No. of Plates (8.0metres) = 1.48 lengths for 1 plate 5.4 m = 1.48 lengths x 2 for top & bottom plates = 2.96 round up to 3 = 3 lengths of 90 x 45 Radiata Pine @ 5.4 metres long

8.0 metres

Tim

ber s

tud

wal

l

Tim

ber s

tuds

Top

plat

e

Bot

tom

pla

te

How are materials measured (Quantity or Number of Bricks)

• Calculate the quantity of bricks required for the double brick building detailed below

(Allow 50 bricks per metre²)

12.0 metres

2.4

met

res

110 mm brickwork

110 mm brickwork

Area of brick wall = length x height

Area of brick wall = 12.0 x 2.4 = 28.8 m²

Area of 2 brick walls = 28.8 x 2 = 57.6 m²

No. bricks = wall area x No. of bricks/m²

No. of bricks required = 57.6 x 50 bricks

No. of bricks = 2880 Bricks

Plan view

Elevation

How are materials measured (Calculate The Cost Of Bricks)

• Calculate the cost of bricks required for the double brick building detailed below

(Bricks to cost $810 per 1000 bricks)

12.0 metres

2.4

met

res

110 mm brickwork

110 mm brickwork

Cost = (No. of bricks) x cost

Cost = (2880 bricks) x $810.00

Cost = 2.88 x $810.00

Cost = $2332.80

Plan view

Elevation Quantity

1000

Materials units • General timber comes in set lengths in increments of

300mm • Put 0.300 in your calculator & press ++ it should

increase by 0.3 of a metre every time you hit the equals button (This is a good way of remembering orderable lengths of timber available at the timber yard)

• Lengths range from 1800mm to 7200mm • Brickwork is measured by 1000 bricks or per pallet • Concrete is measured in cubic metres • Surface area measurements are in metres²

When ordering timber

• Start with the section size e.g. 90mm x 45mm • How the timber is finished e.g. (RS) rough sawn • Species of timber e.g. hardwood • Strength grading e.g. F8 • Number of pieces e.g. 5/6.0 • Order the longest lengths first & progress down to

the shortest • 90 x 45 RS hardwood F8 5/6.0 7/4.8 2/2.4 1/1.8

Rewrite the following Timber orders 2/6.1, 3/4.3, 9/5.0, 3/4.9, 5/2.3

90 x 45 F24 hardwood RS cost $ 3.50 per Lin/M • Answer = 90 x 45 RS Hardwood F24 2/6.3m,

12/5.1m, 3/4.5m, 5/2.4m •Lin metre length = no. x length

•Lineal metre length =2 x 6.3 = 12.6 metres

•Lin metre length =12 x 5.1 = 107.1 metres

•Lineal metre length =3 x 4.5 = 13.5 metres

•Lineal metre length = 5 x 2.4 = 12.5 metres

Total lineal metre length = 145.7 Lin/ Metres Cost = total Lin/M x Cost per Lin/Metres

Cost = 145.7 Lin/M x $3.50per Lin/M

Cost = $509.95

NOTE :Round up to the next increment of 0.3 of a metre e.g. 2.4 metres long

How are materials measured (Surface Area Rectangular Prism) ?

Surface Area is measured in mm² or Metres² SA= (area of base x 2) + (area of one side x 2) +

(area of one end x 2) SA =(4.0 x 2.0 x 2) + (4.0 x 3.0 x 2) + (3.0 x2.0 x 2) SA = (16) + (24) + (12) SA = 52 metres²

4.0 metres

3.0

met

res NOTE: Imagine you cut a box

down all corners & ended up with 6 sides then worked out the area of each side and added them together for a Total Area

How are materials measured (Surface Area Cone) ?

Surface Area is measured in mm² or Metres² Cone SA = (pie x R x length of incline) + ( pie x R²) Cone SA = (3.14 x 0.600 x 2.0) + (3.14 x 0.600²) Cone SA = (3.77) + (1.13) Cone SA = 4.9 metres² Note: Refer to page 159 of your text book for more information

0.600 Radius

2.0

met

res

How are materials measured (Surface Area Of A Cylinder) ?

Surface Area is measured in mm² or Metres² Cylinder SA= (Pie x R² x 2) + (2 x Pie x R x Height) Cylinder SA=(3.14 x 0.800² x 2) + (2 x 3.14 x 0.800 x 3.0) Cylinder SA= (4.02) + (15.08) Cylinder SA= 60.62 metres² Note: Refer to page 159 of your text book for more information 0.800m

Radius

3.0

met

res

How are materials measured (Surface Area Pyramid) ?

Surface Area is measured in mm² or Metres² Pyramid SA = (area of base) + (length of base ) x Inclined height x 4

Pyramid SA = (1.5 x 1.5) + (l.5 ) x 2.0 x 4 Pyramid SA =(2.25) +(0.75) x 8.0 Pyramid SA = 24 metres²

2.0

met

res

2

Note: Refer to page 159 of your text book for more

information

2

How are materials measured (Fractions & Percentages) ?

Percentages can be converted to fractions as follows: • 75 % can be entered into the calculator as 0.75 or 3 abc 4 function on the calculator • Therefore to convert a fraction to a percentage you

can divide 3 ÷ 4 = 0.75 or 75% or on the calculator 3 abc 4 then the equals button then the abc button will give you the same answer 0.75 or 75 %