Image Source: Google ImagesConcreters, Air Conditioning Technicians,Plumbers, Chemical Engineers, RoadTanker Designers, Swimming Pool owners,Medical Staff administering drugs, andmany other people need to know how toaccurately calculate Volumes.
How many 1cm3 cubes will fill theRectangular prism ?The Volume of a 3D Shape is the number of cubesneeded to fill the inside of the shape.Sixteen 1cm3 cubesImage Source: Google Images
How many cubes does this Prism hold?Rather than count all thecubes, we can find theVolume of this prism bycounting how many cubeslong, wide and tall the prismis, and then Multiplying.V = 5 x 3 x 1 = 15There are 15 cubes in the prism, which means thevolume of the Rectangular Prism is 15 cubic units.
How many cubes does this Prism hold?Rather than count all thecubes, we can find theVolume of this prism bycounting how many cubeslong, wide, and tall the prismis, and then Multiplying.V = 5 x 3 x 2 = 30There are 30 cubes in the prism, which means thevolume of the Rectangular Prism is 30 cubic units.
How many cubes does this Prism hold?Rather than count all thecubes, we can find theVolume of this prism bycounting how many cubeslong, wide, and tall the prismis, and then Multiplying.V = 6 x 4 x 3 = 72There are 72 cubes in the prism, which means thevolume of the Rectangular Prism is 72 cubic units.
4 cm x 3 cm x 1cm = 12 cm3Length x Width x Height = Volumearea ofbasex height = volumeFor any Rectangular prism, the Volume isfound by multiplying the Area of its basetimes its Height.1 cm4 cm3 cmHeightLengthWidthV = Area x HeightV = L x W x H
5 cm7 cm10 cmV = Area x HeightV = L x W x HV = L x W x HV = 10 x 7 x 5V = 350 cm3
CylinderCuboid orRectangularPrismTriangular PrismTrapezoid PrismVolume of Prism = Area of Base x HeightArea of Base3D Images Sourced from : http://colleenyoung.wordpress.com/
Area of Circle = π x R2RArea of Rectangle= Length x WidthWLbhArea of Triangle= ½ x base x heighthbArea of Trapezium= ½ x (a + b) x ha
Area of Triangle = ½ x b x h= ½ x 8 x 4Volume = Area x Height between triangle ends= 16 x 6= 96 cm38 cm6 cm4 cm4.9cm= 16 cm23D Image Sourced from : http://colleenyoung.wordpress.com/
Area of Trapezium Base = ½ x(a + b) x h= ½ x (1.5 + 6.5) x 4.28 cm6.5cm4.2 cm= 16.8 cm2(Do not round off decimal areas)Volume = Area x Height between trapezium ends= 16.8 x 8= 134.4 cm3= 134 cm33D Image Sourced from : http://colleenyoung.wordpress.com/
5cm3cmArea of Circle Base = π x R2= π x 32= 28.2743…..cm2Volume = Height x Area of Circle= 5 x 28.2743….= 141 cm3Use full calculator ‘ANS’for Area= 141.3716….cm3(Do not round off decimal areas)3D Image Sourced from : http://colleenyoung.wordpress.com/
1.6 mFor these types, wehave to be given theArea of the Base.We then use V = A x HArea = 24 m2Volume = Area of Irregular Base x Height= 24 x 1.6= 38.4 m3= 38 m3Image Source: www.cheappools.com.au
LHWV = L x W x HorV = LWHBase bheight hV = ½ x b x h x HorV = ½bhHPrism Height HRV = π x Rx R x HorV = πR2H
8 cm6 cm4 cmV = L x W x HV = 8 x 4 x 6V = 192 cm3V = L x W x HorV = LWH
6 m4mV = ½ x b x h x HorV = ½bhHV = ½ x b x h x HV = ½ x 6 x 4 x 10V = 120 m3
8 mm3 V = π x R x R x HorV = πR2HV = π x R x R x HV = π x 3 x 3 x 8V = 226.1946 mm3V = 226 mm3
If we have a container filled with liquid or gas,the Volume is specified in “Capacity” units.Capacity units are Millilitres (mL), Litres (L),Kilolitres (kL) and Megalitres (ML).1 mL = 1 cm3 1 L = 1000 cm31 L = 1000 mL1 ML = 1 000 000 L1 m3 = 1000 L1 L of Water weighs 1 kg
A cylindrical can of Coca Cola has avolume of 375cm3, but is labeled as375mL because it contains liquid.
The city of Melbourne’s main water storage (TheThomson Dam) has a capacity of 1.07 million ML .1 070 000 000 000 x 1 litre bottles of Coca Cola
In the Metric System, Capacity is based on the Litre or “L” unit.ML kL L mLx 1000 x 1000 x 1000÷ 1000 ÷ 1000 ÷ 100032ML = ? L Need to x 1000 twice 32 x 1000 x 1000 = 32 000 000 LCAPACITY conversions use 1000’s, and usually create fairly large results.The Volume of Liquids and Solids is usually measured as a “Capacity”.
It can be seen in the above photo that we have a rectangular prism shaped Trench, containing acylindrical shaped Pipe. Cement is delivered in cubic meters, and the workers would need to havecalculated how much cement needed to be delivered for the job.In this calculation they would need to have done Rectanglar Trench Volume minus the Volume ofthe cylinder Pipe.If they did not do this calculation carefully and correctly, then they would either have too muchcement, (which is expensive to dispose of), or not enough cement which could mean that theywould not be able to complete the job on time.Image Source: http://alkispapadopoulos.com
http://passyworldofmathematics.com/All slides are exclusive Copyright of Passy’s World of MathematicsVisit our site for Free Mathematics PowerPoints