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Measuring volume
The volume of a solid can be measured by calculating how many unit cubes are needed to fill it.
The basic unit of volume is \latex{ 1 } \latex{cubic} \latex{metre} (\latex{ m^{3}}), which is the volume of a cube with \latex{ 1 } \latex{ m } long edges.
\latex{ cubic } \latex{ metre }
\latex{ 1 } \latex{ mm^{3} }
Volume of
the cube
the cube
Name of the unit
\latex{ cubic } \latex{ millimetre }
\latex{ cubic } \latex{ centimetre } \latex{ (millilitre) }
\latex{ cubic } \latex{ decimetre } \latex{ (litre) }
Length of the
edges of the cube
edges of the cube
\latex{ 1 } \latex{ mm }
\latex{ 1 } \latex{ cm }
\latex{ 1 } \latex{ dm }
\latex{ 1 } \latex{ m }
\latex{ 1 } \latex{ m^{3} }
\latex{ 1 } \latex{ dm^{3} } (\latex{ = 1 } \latex{ l })
\latex{ 1 } \latex{ cm^{3} } (\latex{ = 1 } \latex{ ml })
US units of volume:
\latex{ 1 } \latex{ pint } \latex{\approx} \latex{ 47 } \latex{ cl }
\latex{ 1 } \latex{ gallon } \latex{\approx} \latex{ 3.8 } \latex{ l }
\latex{ 1 } \latex{ pint } \latex{\approx} \latex{ 47 } \latex{ cl }
\latex{ 1 } \latex{ gallon } \latex{\approx} \latex{ 3.8 } \latex{ l }
volume
value
unite
\latex{ m^{3} }
\latex{ 1 }
649479
When measuring the volume of liquids, \latex{ litre } is often used instead of \latex{ dm^{3} } (\latex{ 1 } \latex{ dm^{3}=1} \latex{ litre }).
\latex{ 1 } \latex{ litre = 10 } \latex{ dl = 100 } \latex{ cl = 1,000 } \latex{ ml }
Abbreviations: \latex{ hectolitre } – \latex{ hl }; \latex{ litre } – \latex{ l }; \latex{ decilitre } – \latex{ dl }; \latex{ centilitre } – \latex{ cl }; \latex{ millilitre } – \latex{ ml }.
Abbreviations: \latex{ hectolitre } – \latex{ hl }; \latex{ litre } – \latex{ l }; \latex{ decilitre } – \latex{ dl }; \latex{ centilitre } – \latex{ cl }; \latex{ millilitre } – \latex{ ml }.
The units of volume:
\latex{\times1,000,000,000}
\latex{1\;\textcolor{#E3004F}{ml}\;\;\lt\;\;1\;\textcolor{#E3004F}{cl}\;\;\lt\;\;1\;\textcolor{#E3004F}{dl}\;\;\lt\;\;1\;\textcolor{#E3004F}{litre}\;\;\lt\;\;1\;\textcolor{#E3004F}{hl}}
\latex{10 \;dl = 1\;litre}
\latex{100 \;litres = 1\;hl}
\latex{100 \;litres = 1\;hl}
\latex{1,000 \;mm^{3} = 1\;cm^{3}}
\latex{1,000 \;cm^{3} = 1\;dm^{3}}
\latex{1,000 \;cm^{3} = 1\;dm^{3}}
\latex{1,000 \;dm^{3} = 1\;m^{3}}
\latex{1,000,000,000 \;m^{3} = 1\;km^{3}}
\latex{1,000,000,000 \;m^{3} = 1\;km^{3}}
\latex{1 \;hl = 100\;litres = 1,000\;dl = 10,000 \;cl = 100,000\; ml}
\latex{1 \;m^{3} = 1,000\;dm^{3}= 1,000,000\;cm^{3}= 1,000,000,000\;mm^{3}}
\latex{1\;\textcolor{#E3004F}{mm^{3}}\;\;\lt\;\;1\;\textcolor{#E3004F}{cm^{3}}\;\;\lt\;\;1\;\textcolor{#E3004F}{dm^{3}}\;\;\lt\;\;1\;\textcolor{#E3004F}{m^{3}}\;\;\;\;\;\lt\;\;\;\;\;1\;\textcolor{#E3004F}{km^{3}}}
\latex{\times100}
\latex{\times1,000}
\latex{\times1,000}
\latex{\times1,000}
\latex{\times10}
\latex{\times10}
\latex{\times10}
Exercises
{{exercise_number}}. The ant can only measure in \latex{ cubic } \latex{ millimetres }, the mouse in \latex{ cubic } \latex{ centimetres }, the rabbit in \latex{ cubic } \latex{ decimetres } and the elephant in \latex{ cubic } \latex{ metres }.
Convert the following amounts into their units.
Convert the following amounts into their units.
a) \latex{ 31 } \latex{ cm^{3} }
b) \latex{ 14 } \latex{ cm^{3} } \latex{ 9,300 } \latex{ mm^{3} }
c) \latex{ 3 } \latex{ ml }
d) half a \latex{ cl }
b) \latex{ 14 } \latex{ cm^{3} } \latex{ 9,300 } \latex{ mm^{3} }
c) \latex{ 3 } \latex{ ml }
d) half a \latex{ cl }
a) \latex{ 5,000 } \latex{ mm^{3} }
b) \latex{ 89 } \latex{ cm^{3} } \latex{ 3,500 } \latex{ mm^{3} }
c) \latex{ 67 } \latex{ cl }
d) \latex{ 5 } \latex{ l } \latex{ 34 } \latex{ cl }
b) \latex{ 89 } \latex{ cm^{3} } \latex{ 3,500 } \latex{ mm^{3} }
c) \latex{ 67 } \latex{ cl }
d) \latex{ 5 } \latex{ l } \latex{ 34 } \latex{ cl }
a) \latex{ 9 } \latex{ m^{3} } \latex{ 2,000 } \latex{ cm^{3} }
b) \latex{ 6 } \latex{ litres }
c) \latex{ 5,000 } \latex{ ml }
d) \latex{ 7 } \latex{ hl }
b) \latex{ 6 } \latex{ litres }
c) \latex{ 5,000 } \latex{ ml }
d) \latex{ 7 } \latex{ hl }
a) \latex{ 18, 000 } \latex{ dm^{3} }
b) \latex{ 80 } \latex{ hl }
c) \latex{ 56,000 } \latex{ litres }
d) \latex{ 4 } \latex{ million } \latex{ cm^{3} }
b) \latex{ 80 } \latex{ hl }
c) \latex{ 56,000 } \latex{ litres }
d) \latex{ 4 } \latex{ million } \latex{ cm^{3} }
{{exercise_number}}. Convert the following amounts into
a) \latex{ millilitres }: \latex{ 45 } \latex{ cl }; \latex{ 3 } \latex{ l } \latex{ 23 } \latex{ cl }; \latex{ 70,000 } \latex{ mm^{3} }; \latex{ 4 } \latex{ m^{3} } \latex{85} \latex{cm^3};
b) \latex{ centilitres: } \latex{ 5,100 } \latex{ ml }; \latex{ 4 } \latex{ l } \latex{ 67 } \latex{ cl }; \latex{ 43,000,000 } \latex{ mm^{3} }; \latex{ 2 } \latex{ m^{3} } \latex{ 870 } \latex{ cm^{3} };
c) \latex{ decilitres: } \latex{ 760 } \latex{ cl }; \latex{ 7 } \latex{ l } \latex{ 50 } \latex{ cl }; \latex{ 200,000 } \latex{ mm^{3} }; \latex{ 34,000 } \latex{ cm^{3} };
d) \latex{ litres }: \latex{ 600 } \latex{ dl }; \latex{ 9 } \latex{ hl }; \latex{ 72,000,000 } \latex{ mm^{3} }; \latex{ 7 } \latex{ m^{3} }; \latex{ 211,000 } \latex{ cm^{3} };
e) \latex{ hectolitres }: \latex{ 400 } \latex{ litre }; \latex{ 8,300 } \latex{ litre }; \latex{ 5 } \latex{ m^{3} }; \latex{ 8 } \latex{ m^{3} } \latex{ 300,000 } \latex{ cm^{3} }.
b) \latex{ centilitres: } \latex{ 5,100 } \latex{ ml }; \latex{ 4 } \latex{ l } \latex{ 67 } \latex{ cl }; \latex{ 43,000,000 } \latex{ mm^{3} }; \latex{ 2 } \latex{ m^{3} } \latex{ 870 } \latex{ cm^{3} };
c) \latex{ decilitres: } \latex{ 760 } \latex{ cl }; \latex{ 7 } \latex{ l } \latex{ 50 } \latex{ cl }; \latex{ 200,000 } \latex{ mm^{3} }; \latex{ 34,000 } \latex{ cm^{3} };
d) \latex{ litres }: \latex{ 600 } \latex{ dl }; \latex{ 9 } \latex{ hl }; \latex{ 72,000,000 } \latex{ mm^{3} }; \latex{ 7 } \latex{ m^{3} }; \latex{ 211,000 } \latex{ cm^{3} };
e) \latex{ hectolitres }: \latex{ 400 } \latex{ litre }; \latex{ 8,300 } \latex{ litre }; \latex{ 5 } \latex{ m^{3} }; \latex{ 8 } \latex{ m^{3} } \latex{ 300,000 } \latex{ cm^{3} }.
{{exercise_number}}. Which one is greater?
a) \latex{ 56 } \latex{ litres } or \latex{ 4,800 } \latex{ cl }
b) \latex{ 3 } \latex{ litres } or \latex{ 400 } \latex{ cm^{3} }
c) \latex{ 790 } \latex{ litres } or \latex{ 8 } \latex{ hl }
d) \latex{ 670 } \latex{ ml } or half a \latex{ litre }
e) \latex{ 5 } \latex{ ml } or \latex{ 500 } \latex{ mm^{3} }
f ) \latex{ 94 } \latex{ m^{3} } or \latex{ 95 } \latex{ hl }
{{exercise_number}}. Choose the most probable answer.
a) A car’s fuel tank is \latex{ 500 } \latex{ l }; \latex{ 5 } \latex{ hl }; \latex{ 50 } \latex{ l }.
b) A bathtub is \latex{ 2 } \latex{ l }; \latex{ 20 } \latex{ l }; \latex{ 200 } \latex{ l }.
c) A coffee cup is \latex{ 8 } \latex{ cl }; \latex{ 8 } \latex{ l }; \latex{ 20 } \latex{ ml }.
d) A cooking pot is \latex{ 4 } \latex{ l }; \latex{ 34 } \latex{ hl }; \latex{ 54 } \latex{ ml }.
{{exercise_number}}. The ingredients of a raspberry pie are:
half a cup of sugar • \latex{ 1 } tablespoon of lemon juice • \latex{ 2 } and a half cups of dried raspberries • half a cup of raspberry juice • \latex{ 2 } and a half tablespoons of flour • teaspoon of cinnamon • \latex{ 1 } tablespoon of oil.
Estimate the volume of the ingredients in \latex{ millilitres }.
{{exercise_number}}. Lake Balaton contains about \latex{ 2 } \latex{ billion } \latex{ m^{3} } of water. Convert this amount into \latex{ cubic } \latex{ kilometres } and \latex{ hectolitres }.
{{exercise_number}}. When do you use more water? If you take a bath in a tub filled with \latex{ 200 } \latex{ dm^{3} } of water, or if you take a shower for \latex{ 5 } \latex{ minutes } using \latex{ 15 } \latex{ litres } of water \latex{ per } \latex{ minute? }
Quiz
Can the entire population of the Earth be fitted into a cube with a volume of \latex{ 1 } \latex{ km^{3}?}
