Basic Measuring and Calculations. Formulas, Workings Hints and Tips

Transcription

1 Basic Measuring and Calculations Formulas, Workings Hints and Tips

2 Start by writing down the formula When working out mathematics 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

3 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

4 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 metres to millimetres x by 1000 = 1000 millimetres To convert from millimetres to metres e.g millimetres 1000 = metres For more information refer to page 151 of your text book table 5.1

5 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

6 (Lineal measurement)? Linear measurements are measured in mm or metres e.g. measuring the length of a wall is measured in lineal metres metres Brick wall Therefore the lineal length of the brick wall is metres long

7 (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 metres metres Formula = P1 + P2 + P3 + P4 = Total lineal metres The total length around the room = = 14 lineal metres

8 (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 Radius 1.5 m Circumference of a circle = 2 x pi x r Circumference = 2 x 3.14 x 1.5 Circumference = 9.42 metres Water tank NOTE : The answer is measured in metres only because there is only one measurement in the equation

9 Area Formulas

10 (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) Area = L x W 2.0 metres Swimming pool cover 6.0 metres Area = 6.0 x 2.0 Area = 12.0 metres² Note : The answer is in metres² because there are two measurements in the equation

11 (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 5.0 metres Area A Area B 3.0 metres 2.0 metres 2.0 metres Area A = 5.0 x 2.0 Area A = 10.0 metres² Area B = L x W Area B = 3.0 x 2.0 Area B = 6.0 metres² Total Area A + B = =16 m²

12 (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 Diameter 4.0 m Radius 2.0 m Cover for circular swimming pool Area = 3.14 x 2.0² Area = metres² Note : The answer is in metres² because there are two measurements in the equation (Pie & Radius)

13 (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) 3.0 metres Cover for triangle shaped swimming pool 4.0 metres 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

14 (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 1.5 metres 2.0 metres 3.0 metres Cover for irregular shaped swimming pool 2 Area = ( ) x 1.5 Area = 4.0 metres² 2 2 Note : The answer is in metres² because there are two measurements in the equation

15 (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) Amount of water in the swimming pool Volume = L x W x D Volume = 6.0 x 2.0 x 1.5 Volume = 18.0 metres³ 1.5 m Note : The answer is in metres³ because there are three measurements in the equation

16 (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) 1. 0 m radius 3.0 metres Amount of water in water tank tank 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

17 (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) 2.0 metres Amount of oxygen inside the tent 3.0 metres 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

18 (Odd Shapes Volume)? Calculate the lineal length of concrete footings required & how much concrete is needed in metres³ 4.0 metres NOTE : Footing depth m x wide 5.0 metres m wide footing 2.0 metres 2.0 metres Length = footing length footing width Side 1 = = 4.4m Side 2 = = 1.4m Side 3 = = 2.0m Side 4 = = 2.0m Side 5 = = 2.4m Side 6 = = 3.4m= 15.6Lin/M Volume = Lineal length x width x depth 3.0 metres Volume = 15.6 x x = 3.74m³

19 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

20 (Quantity or Number of Studs)? No. of studs (length of wall) + 1 (Extra stud) Stud spacing No. of studs (8.0metres) = say = 15 studs m Timber stud wall 8.0 metres

21 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

22 (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 5.4 metres long Top plate Bottom plate Timber stud wall Timber studs 8.0 metres

23 (Quantity or Number of Bricks) Calculate the quantity of bricks required for the double brick building detailed below 2.4 metres Plan view Elevation 12.0 metres 110 mm brickwork 110 mm brickwork (Allow 50 bricks per metre²) 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

24 (Calculate The Cost Of Bricks) Calculate the cost of bricks required for the double brick building detailed below Plan view Elevation (Bricks to cost $810 per 1000 bricks) 110 mm brickwork 110 mm brickwork Cost = (No. of bricks) x cost Quantity 2.4 metres 12.0 metres Cost = (2880 bricks) x $ Cost = 2.88 x $ Cost = $

25 Materials units General timber comes in set lengths in increments of 300mm Put 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

26 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

27 Cost = $ Rewrite the following Timber orders 2/6.1, 3/4.3, 9/5.0, 3/4.9, 5/ 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 = 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 = Lin/ Metres Cost = total Lin/M x Cost per Lin/Metres Cost = Lin/M x $3.50per Lin/M NOTE :Round up to the next increment of 0.3 of a metre e.g. 2.4 metres long

28 (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 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 3.0 metres 4.0 metres

29 (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 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 Radius 2.0 metres

30 (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 x 3.0) Cylinder SA= (4.02) + (15.08) Cylinder SA= metres² Note: Refer to page 159 of your text book for more information 3.0 metres 0.800m Radius

31 Note: Refer to page 159 of your text book for more information 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 Pyramid SA =(2.25) +(0.75) x 8.0 Pyramid SA = 24 metres² 2.0 metres

32 (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 %