VOLUME

By Moira Whitehouse PhD

•MATTER HAS MASS AND WEIGHT, BUT IT ALSO TAKES UP SPACE.

•MATTER HAS MASS AND WEIGHT, BUT IT ALSO TAKES UP SPACE.

•TWO PIECES OF MATTER CANNOT OCCUPY THE SAME SPACE AT THE SAME TIME.

•THINK ABOUT IT, YOU ALREADY KNOW THAT TWO THINGS CANNOT BE IN THE SAME SPACE AT THE SAME TIME?

•THE AMOUNT OF SPACE SOMETHING TAKES UP IS CALLED ITS

VOLUME.

•TO FIND AN OBJECT’S VOLUME, WE MEASURE THE SPACE IT TAKES UP.

•WHATEVER UNIT WE USE TO MEASURE LENGTH, WE WILL MAKE INTO A CUBE TO DESCRIBE THE SPACE AN OBJECT TAKES UP, ITS VOLUME.

•TO DO THAT WE WILL NEED TO SELECT SOME STANDARD UNIT WITH WHITCH TO MEASURE.

•A CUBE MADE WITH METER STICKS WOULD BE ONE CUBIC METER.

ONE CUBIC METER ORONE METER CUBED

•IN SCIENCE, ONE STANDARD UNIT FOR MEASURING VOLUME IS THE SPACE IN ONE CENTIMETER CUBED.

•ONE CUBIC CENTIMETER

•THE VOLUME OF AN OBJECT OR THE VOLUME OF A SPACE DESCRIBES.... HOW MANY CUBIC CENTIMETERS WOULD FILL ALL THE SPACE IN IT.

•WHAT IS THE VOLUME OF THIS CUBE?

1 CM X 1 CM X 1 CM =1 CUBIC CENTIMETER (CC)

•WHAT IS THE VOLUME OF THIS STRING OF 10 CUBES?

1 CM X 1 CM X 10 CM =10 CM CUBIC CENTIMETERS (CC)

•THIS OBJECT HAS 10 CENTIMETERS ON TWO SIDES.WHAT IS ITS VOLUME?

1 CM X 10 CM X 10 CM =100 CUBIC CENTIMETERS (CC)

•NEXT WE SEE A LARGE CUBE WITH10 CM ON EACH SIDE.WHAT IS THEVOLUME OF THIS CUBE?

10 CM X 10 CM X 10 CM = 1000 CUBIC CENTIMETERS (CC)

•HERE WE HAVE A PLASTICCONTAINER THESAME SIZE AS THE LARGE BLUECUBE.

•WHAT IS THE VOLUME OR CAPACITY OF THIS CONTAINER?

•IF YOU SAID 1000 cc YOU WOULD BE CORRECT. 1000 mL

•BUT WHY IS IT LABELEDWITH mLINSTEAD OF cc?

•BECAUSE THE LIQUID MEASURE “LITER” WHICH IS 1000 mL IS EXACTLY THE SAME VOLUME AS “1000 CUBIC CENTIMETERS.”•SO, THE LITER OF GINGER ALE SHOULD FIT EXACTLY INTO THE 1000 cc CONTAINER.

•AND IT DOES.

•THEREFORE,

CUBIC CENTIMETERS (cc) AND MILLILITERS (mL)

ARE TWO NAMES FOR THE SAME AMOUNT OF VOLUME.

•AN EMPTY CUBE WITH 1 cm SIDES WOULD HOLD 1 CUBIC CENTIMETER (cc) OR 1 MILLILITER (mL) OF LIQUID.

SYRINGES USED BY MEDICAL PROFESSIONALS TO MEASURE MEDICINE ARE CALIBRATED IN CUBIC CENTIMETERS (cc).

•EXACTLY ONE cc OF WATER IN A SYRINGE PERFECTLY FILLS A CUBIC BOX WITH SIDES AND BOTTOM OF ONE CENTIMETER.

•THE STANDARD UNITS OF VOLUME “cc” AND “mL” REFER TO THE AMOUNT OF SPACE, NOT THESHAPE OF THESPACE.

THIS MEASURING SPOON HOLDS 1cc OF WATER.

•AND THIS MEASURING SPOON HAS A 1cc CUBE OF PLASTICRESTING INIT.

THE SHAPES ARE DIFFERENT, BUT THE VOLUME IN EACH SPOON IS THE SAME.

•THIS 25 cc MEASURING SPOON WOULD HOLD 24 MORE OF THESE CUBES IF THEY WERE MELTED INTO A LIQUID.

•LET’S NOW CONSIDER SOME WAYS TO MEASURE VOLUME.

•REMEMBER HOW LENGTH IS MEASURED?

•REMEMBER HOW WEIGHT IS MEASURED?

•AND HOW MASS IS MEASURED?

•BUT THE VOLUMES OF SOLIDS,LIQUIDSAND GASESMUST ALL BE MEASURED DIFFERENTLY.

•THE VOLUME OF REGULAR SOLIDS CAN BE FOUND WITH A FORMULA.•BUT TO FIND THE VOLUME OF SOLIDS OF ANY SHAPE WE CAN ALWAYS USE DISPLACEMENT.

•FIRST, FORUMLAS: TO FIND THE VOLUME OF A RECTANGULAR PRISM WE WILL USE THE FORMULA: V = L X W X H.

•SO V = 5 X 4 X 5.

•5 X 4 = 20 X 5 = 100` V =

100 cc•FOR THE DISBELIEVERS, THERE ARE 100 CUBES, COUNT ‘EM.

•WE’LL NOW USE THE FORMULA TO FIND THE VOLUME OF THIS PAPERCLIP BOX.

•V = L X W X H.•V = 7 X 5 X 2.•V = 70 cc

•CAREFULLY FILLING THE BOX, WE FIND THAT TWO LAYERS OF CUBES 5 cm BY 7 cm EXACTLY FILL THE BOX.

•COUNTING THE CUBES WE FIND 35 IN THE TOP LAYER AND 35 IN THE BOTTOM LAYER, A TOTAL OF 70 CENTIMETER CUBES THAT EXACTLY FILL THE BOX.

•PROVING AGAIN THAT THE FORMULA WORKS FOR REGULAR SOLIDS.

•BUT WHAT IF A SOLID IS IRREGULARLY SHAPED, LIKE A ROUGH ROCK?•HOW CAN WE FIND THE VOLUME OF SUCH AN OBJECT IF THERE IS NO FORMULA?•REMEMBERING THAT TWO THINGS CAN NOT BE IN THE SAME PLACE AT THE SAME TIME, WE WILL USE DISPLACEMENT.

•IF THE ROCK IS PLACED IN THE WATER, SOME WATER MUST MOVE OUT OF ITS WAY.•HOW MUCH?•EXACTLY THE SAME AMOUNT AS THE VOLUME OF THE ROCK.

•BY NOTING THE INCREASE IN THE WATER LEVEL, WE WILL KNOW THE VOLUME OF THE ROCK.

20 mL

IS THE SAME VOLUME AS

•SO, THE VOLUME OF THE ROCK...

•SUPPOSE WE WANT TO MEASURE THE VOLUME OF THIS ROCK USING DISPLACEMENT.

•BEFORE PLACING THE ROCK IN THE BEAKER, NOTICE THAT THE WATER LEVEL IS 500 mL.

•WHEN WE PLACE THE ROCK IN THE BEAKER, THE WATER LEVEL RISES TO 600 mL.

•WHAT IS THE VOLUME OF THE ROCK?

•THIS IS A RECTANGULAR PRISM MEASURING 10 cm BY 5 cm BY 2 cm WITH A VOLUME OF

•NOW LET’S CHECK ITS VOLUME USING DISPLACEMENT.

•100 cc.

•BEFORE PLACING THE PRISM IN THE WATER, NOTE THE WATER LEVEL IS AT 600 mL. •WHAT WILL THE WATER LEVEL BE WHEN THE PRISM IS PLACED IN THE WATER?

•THE WATER LEVEL RISES TO 700 mL.

•WHAT IS THE PRISM’S VOLUME?

•SO WHAT’S THE RELATIONSHIP BETWEEN THE VOLUME OF THE ROCK AND THE RECTANGULAR PRISM?

•WHAT DO YOU THINK WOULD BE THE RELATIONSHIP BETWEEN THEIR MASSES?

•THIS ROCK AND THIS RECTANGULAR PRISM HAVE THE SAME VOLUME—100 cc OR 100 mL.

•HOWEVER, THE ROCK WOULD HAVE MORE MASS THAN THE PRISM.

•THE VOLUME OF A LIQUID CAN BE FOUND BY PLACING IT IN A GRADUATED CYLINDER AND READING THE VOLUME.

NOW IS THE TIME TO MEASURE THE VOLUME OF SOME LIQUIDS.

WHAT IS THE VOLUME OF THE BLUE LIQUID IN THIS GRADUATED CYLINDER?

mL

HOW MANY MELTED 1 CUBIC CENTIMETERS CUBES WOULD IT TAKE TO FILL THE GRADUATED CYLINDER TO THIS LEVEL?

WHAT IS THE VOLUME OF THE BLUE LIQUID IN THIS GRADUATED CYLINDER?

mL

HOW MANY MELTED 1 CUBIC CENTIMETERS CUBES WOULD IT TAKE TO FILL THE GRADUATED CYLINDER TO THIS LEVEL?

WHAT IS THE VOLUME OF THE BLUE LIQUID IN THIS GRADUATED CYLINDER?

WHAT IS THE VOLUME OF THE BLUE LIQUID IN THIS SYRINGE?

WHAT IS THE VOLUME OF THE BLUE LIQUID IN THIS SYRINGE?

•THE VOLUME OF A GAS IS FOUND BY KNOWING THE VOLUME OF ITS CONTAINER SINCE GASES EXPAND TO FILL WHATEVER CONTAINER THEY ARE IN.

•SINCE THE UNITED STATES IS ABOUT THE ONLY COUNTRY NOT USING THE METRIC SYSTEM FOR DAILY TRADING ACTIVITIES, WE SHOULD HAVE SOME IDEA OF VOLUME MEASURES IN OTHER COUNTRIES.

•HERE WE WILL COMPARE SOME FAMILIAR CONTAINERS IN THE ENGLISH AND METRIC SYSTEM OF MEASUREMENT:

•IF YOU NOW HAVE THE IDEA THAT THE AMOUNT OF SPACE AN OBJECT TAKES UP IS ITS VOLUME....

YOU’VE GOT THE IDEA.