Volume and capacity – millilitres and litres and capacity – millilitres and litres 1 When we convert: a millilitres to litres, we by 1000 b litres to millilitres, we by Convert
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d Paulaismakingapunchforherparty.Sheuses1.5Loforangejuice,750mLpineapplejuice,1.25Loflemonadeand1.25Lofgingerale.Howmuchpunchdoesshehavealtogether?Howmany250mLcupswillshebeabletofill?
How much liquid is in each jug? Answer in both litres and millilitres. The first one has been done for you.
Fill the jugs below to the amount shown:
Below is a recipe for the delicious summer drink, Lava Flow. The capacity measurements are expressed in cups or teaspoons. Express them in millilitres:
Lava FlowIngredients (for one drink)
•12 cupofpineapplejuice _______ mL
•12 cup of cream _______ mL
•12 a banana
•3teaspoonsofcoconutcream _______ mL
•4strawberries
•1cupice _______ mL
If you were going to make this drink for your entire class, what amounts of each ingredient would you need to purchase? Use a calculator if you wish. What is the most effective unit in which to express the amounts?
a ________ L
________ mL
b ________ L
________ mL
c ________ L
________ mL
d ________ L
_________ mL
e ________ L
________ mL
a 600 mL b 0.4 L c 1800 mL d 1.6 L e 500 mL
1 L
1 L 1 L2 L
1 L
2 L
1 L
1 L
1 L 1 L1 L 1 L
These capacity measurements are useful to know: 1 teaspoon = 5 mL 1 cup = 250 mL
Use the formula L × W × H = V to find the volume of these prisms. You may use a calculator.
a b c d
Boxes of tissues are packed in cubic metre containers to be shipped to supermarkets. Use a calculator to work out how many of these boxes will fit into each container. You will first need to work out how many cubic centimetres are in a cubic metre.
Work with a friend on this activity. You may either physically build the towers or choose to talk through the problem together. You are building towers using centicubes. One of you makes your first level with 4 rows of 3 blocks. The other person starts with 5 rows of 4 blocks. The first one has been done for you.
a Fill in the table to show how the volume of thetowerswouldincreaseastheygrow.
b Your teacher says you can only have 200 cubes between you. You build the towers to the same height.Howmanylevelscouldyoueachbuild?
_____________________________________
_____________________________________
_____________________________________
Person 1 Person 2
1st level 12 cm3 20 cm3
2nd level cm3 cm3
3rd level cm3 cm3
4th level cm3 cm3
5th level cm3 cm3
6th level cm3 cm3
7th level cm3 cm3
8th level cm3 cm3
Shape a b c d
Volume
a
________________boxes
b
________________boxes
c
________________boxes
10 cm
20 cm10 cm
10 cm
10 cm10 cm
10 cm25 cm
10 cm
7.5 m
4 m
4 m
3.25 m3 m
4 m
4 m
3.5 m
5 m
4 m
3.5 m
10 m
Volume and capacity – cubic centimetres and cubic metres
Now use the objects below (or something equivalent). Using displacement, find the volume and capacity of each object.
Objecta b c d e f g
Volume
Capacity
Volume and capacity – displacement
Rememberthatvolumeistheamountofspaceoccupiedbyanobjectorsubstanceandcapacityistheamountanobjectwillhold.Displacementistheamountoffluidthatispushedawaywhenanobjectisplacedinthefluid. We can use displacement to calculate both volume and capacity.
1
2
3
Try this experiment to find out about displacement. You will need a jug, a lunchbox, a tray and a model made from 100 centicubes. Work with a friend or in a small group.
Inthisactivityyouaregoingtousewhatyouknowabouttherelationshipbetweenmass and volume to calculate the volume of the water in mud. You will need a cup, some newspaper and a scale.
Workwithapartner.Thisexperimentmaytakeadayorsotocompleteandisprobably best done outside.
Collect a cupful of mud or damp soil. Make sure the mud is not too sloppy. Find its massbyweighingit.Howwillyoudothis?Perhapsyoucouldweightheemptycupandthensubtracttheweightofthecup.
Now spread out your mud onto sheets of newspaper and leave it to dry in the sun. It mayhelptoplaceweightsonthepaperortapeitdown.Youmayalsoneedtolabelyourexperimentsoitdoesn’tgetaccidentallycleanedup!
Once your mud has dried, carefully collect it and measure its mass. Remember to usethesamecup.Whydoyouneedtodothis?
This activity will help you get a feel for different masses. You̕ll need the objects in the table, a calibrated scale or a balance scale and some small masses (10 g, 50 g, or 100 g). Estimate, then measure the mass:
Item Estimate Mass
scissors
gluestick
calculator
lunchbox(full)
lunchbox(empty)
pencil case (full)
pencil case (empty)
Estimate and then measure how many of each of these objects are needed to balance 10 grams.
Centicubes 5¢ Coins Drawing pins
Estimate
Measure
Use your answers in question 1 to place the 7 items on the line in order of their individual mass.
Write each mass in grams, kilograms and grams and as a decimal.
Grams 1000g 350g
Kilograms and grams 2kg700g 5kg50g
Decimal notation 7.125kg 3.2kg
Lightest Heaviest
Weight measures the force of gravity on an object and mass measures its inertia or the amount of matter that can ‘push back’. A brick weighs less in outer space where there is no gravity but its mass stays the same.
c Nextweek,thefootballstartsagain.Theregoesthemarking.MrBrownwillnowbesittinginthegrandstandmunchingchipsandcheeringontheMightyBlues.Ifheconsumesfour375gbagsofchipsinaparticularlytensegame,howmuchdoesheeat?
a Usedecimalnotationtowritethemassesinkilogramsasshownonthescales:
A regular packet of cereal has a mass of 540 g. An average serving is 45 g. Answer these questions without a calculator.
a Howmanyaverageservingsarethereinonepacket? ___________________
b TherearefourpeopleinMichaela’sfamily.Eachhasanaverageserveperday. Howmanydayswilltheboxlast? ___________________
c Thelargestsizedboxhasamassof720g.Howlongwillthisboxlastherfamily? ___________________
d Michaela’sfamilyisgoingcampingfor2weeks.Theyneedtotakeall theirfoodwiththem.Theywanttotakeexactlytherightamountofcereal. Howmanyboxesofeachsizewilltheyneedtotake? ___________________
5 Repeat for 100 mL, 250 mL, 500 mL and 1 L and record your results.
Amount of water 50 mL 100 mL 250 mL 500 mL 1 L
Mass
a Whathaveyoudiscovered?1mLofwater= gram.
b Whydidyouneedtosubtractthemassofthecup? ________________________________________
Without measuring, can you now calculate the mass of these amounts of water?
a 150mL =____________g b 467mL=____________g c 1.5L =__________kg
d 980 mL = ____________kg e 2.75 L = ____________kg f 8.45 L = __________g
Ben poured the same amount of water into five different containers. He then measured the mass of each of them. If you can work out the mass of each of the containers, Ben says your teacher will give you 5 early minutes. All the clues you need are in the table.
Container A B C D E
Mass of container filled with water
365g 678g 458g 1kg 1.3g
Mass of container 15g
How did you go? Did your teacher get the memo about the early minutes?
Try this experiment. You’ll need 10 centicubes, plasticine, a measuring cup and a tap. Push the centicubes gently but fully into the plasticine, then carefully remove them. Now, fill the holes with water. Finally, measure the amount of water.
a Howmuchwaterwasused? _____________________________________________________________
b Wasittheamountyouexpected?Ifnot,whydoyouthinkitisdifferent?
Sean’s teacher asked him to conduct an experiment to find out more about the mass of water.
a Hestartedtodrawthisgraphandtable.Completebothforhim:
b Seanthendecidedtoseewhatwouldhappenwhenhesubmergedcenticubesinthewater.Thisgraphshowshowmuchwaterwasdisplacedashedidthis.Usethegraphtocompletethetable:
c UsetheinformationSeandiscoveredtocompletethefollowingtable: