This will help student to understand what volume is and how volume of a cylinder is calculated. rules of Unit conversion is also described.
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Volume of a Cylinder
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What is Volume? The volume of a three-dimensional figure is the amount of space within it. Measured in Units Cubed (e.g. cm3)
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What is this? ' It has 2 equal shapes at the base, but it is not a prism as it has rounded sides ' It is a Cylinder h
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Volume of a Cylinder ' How might we find the Volume of a Cylinder?
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Example
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Pieces Missing ' Find the volume of concrete used to make this pipe Volume of Concrete = Volume of Big Cylinder— Volume of Small Cylinder (hole) 0.35 m 0.4
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What shape is present here? 1042m
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What 3D shapes can you see? 14 mrn---...................+.l
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HOME WORK cm 162 cm Find the Volume of the Solid. To 1 decimal place
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Homework/ChaIlenge Challenge Question 40 mm 60 50 40 mm 3m mm
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Volume of a Cylinder ' How might we find the Volume of a Cylinder?
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Conversion of units ' lcm— 10mm ' 1m — IOOcm ' Ikm — 1000m
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Conversions of Units 1 cm2 1 m2 1 m2 1 ha 1 km2 = 10 mm x 10 mm = 100 cm x 100 cm = 1000 mm x 1000 mm = 100 m x 100 m = 100 ha =IOO mm2 = 10 000 cm2 = 1 000 000 mm2 = 10 000 m2 x i cooo:o
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What about when cubic units? 1 cm3 ' = lcm x lcm x lcm ' = 10 mm x 10 mm x 10 mm = mm3 , 1m3 ' = 1m x 1m x 1m ' = 100 cm x 100 cm = 1 cm3 -1000 x 1000 mm3 1000
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Capacity ' Volume - The volume of a three-dimensional figure is the amount of space within it. Measured in Units Cubed (e.g. cm3) ' Volume and capacity are related. ' Capacity is the amount of material (usually liquid) that a container can hold. ' Capacity is measured in millilitres, litres and kilolitres. x 1000 * 1000
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Examples of Capacity A can of drink holds 375 mL. A can of paint holds 4 L.
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How does Volume relate to Capacity? 1000 mL=1L 1000 L = 1 kL ' lcm3= 1 mL 1,OOOcm3 = IOOOml = IL 1m3= 1000 L = 1 kL
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Examples ' Convert 1800 mL to L 1800mI = 1800/1000 = 1.81 2.3 m3 to L 2.3m3 = = 23001 1m3 = IOOOL (11
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Capacity ' Find the Capacity of this cube ' Length = 5.53cm = (5.53 x 5.53 = 169.11cm3 ' Capacity = 169.1 Iml Length = 5.53cm (lcm3 = Iml)
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Example 26 em ' Find the capacity of this rectangular prism. Solution Volume = Ah = (26 x 12) = cm3 Capacity = 1560 or 1.56 L (lcm3 = 1mL) (IOOOmL = IL)
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Ex 11.08 -Q 7. nie tank on a fuel tanker is in the shape of a cylinder 6 metres long, with a diameter of 2 metres. a Find, correct to three decimal places, the volume of the tank in cubic metres. b How many litres of fuel ean this tank hold?
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What size rainwater tank would be needed to hold the run-off when 40 mm of rain falls on a roof 12 m long and 3.6 m wide? (Answer in litres.)
Discussion
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