Area & Volume Area is product of 2 units of length metre x metre = m2 Remember if the unit is squared so to is the conversion. 1 m2 = 10002 mm2 = 1000000 mm2 or 1 x 106 mm2 It is important that you are able to find the areas and perimeters of standard shapes Create a simple aid sheet for the following areas and perimeters in the following fashion: eg1. Rectangle (sketch the shape) Area = L x b Perimeter = 2L + 2b Breadth b Length L JR/2008

Area & Volume 2. Parallelogram Use the format shown to create a sheet for the following shapes: 2. Parallelogram 3. Triangle ( please also research Hero’s formula & sine formula) 4. Trapezium 5. Circle 6. Sector of a circle Useful refs :- Greer & Taylor – BTEC National Mathematics for Technicians JR/2008

Area & Volume Volume or Capacity are similar with identical units. Volume found from area x length of area gives units m2 x m = m3 Remember if the unit is cubed so to is the conversion. 1 m3 = 10003 mm3 = 1000000000 mm3 or 1 x 109 mm3 Liquid capacity is often measured in litres ( ℓ ). It must be noted that the litre is an approximate unit ( 1 litre = 1.000028 dm3 ) and should not be used for precise measurements. In general terms 1 m3 = 1000 ℓ To obtain volume it is usual to consider cross sectional area (csa) first , then multiply csa by length of csa. JR/2008

Area & Volume eg. find the volume of a 2m length of round bar of 20mm diameter. Soln. First find csa of bar ( πr2 ) = π x 102 = 314.2 mm2 Converting to m2 = 314.2 ÷ 10002 = 0.0003142 m2 ( or more simply 314.2 x 10-6 m2 ) Remember if the unit is cubed so to is the conversion. Volume = csa x length of csa ( giving πr2 x h (height or length of area) ) Volume = 314.2 x 10 -6 m2 x 2m = 628.4 x 10-6 m3 ( 0.0006284 m3 ) JR/2008

Area & Volume eg2. find the volume (capacity in litres ) of a cylinder 88mm internal diameter (i/d) and 212mm depth. Soln. First find area of cylinder ( πr2 ) = π x 442 = 6082.1 mm2 (1d.p.) Volume = csa x length of csa Volume = 6082.1 mm2 x 212 mm = 1289410.2 mm3 Converting to m3 Remember if the unit is cubed so to is the conversion. 1289410.2 mm3 ÷ 10003 = 0.00128941 m3 if 1000 litres = 1 m3 then 0.00128941 m3 = 0.00128941 x 1000 = 1.289 litres Remember – the litre is an approximate unit JR/2008

Area & Volume One important property related to this work is DENSITY. Density is taken as mass per unit volume, (mass ÷ volume) Density has the symbol ρ (rho) and the unit kg/m3 or kg.m-3 The average density of pure water should be noted as 1000 kg m-3 Density knowledge can be put to good use in engineering eg. Find the mass of steel needed to cast a solid ingot 400mm square x 2m long given the density of steel to be 7600 kg m-3 Soln. Find the volume required = 0.4m x 0.4m x 2m = 0.32 m3 from density = mass/volume (ρ = m/v) then mass = density x volume m = ρ x v giving mass m = 7600 kg m-3 x 0.32 m3 = 2432 kg (2.43 tonne) JR/2008