Transcript: Finding the Volume of a Rectangular Prism
(music plays)
In a colourful TV studio, Shahana stands next to a wall touch screen. She is in her twenties, with shoulder-length brown hair. She wears a blue T-shirt with a print that reads "Home Work Zone" and black trousers.
She says HEY, TVO KIDS.
I'M TEACHER SHAHANA.
AND I'M HERE TODAY TO SHOW YOU
HOW TO FIND THE VOLUME
OF A RECTANGULAR PRISM.
BUT FIRST, WHAT IS VOLUME?
She clicks on a top menu and a definition appears, next to the pictures of a truck and a fridge.
She continues THE VOLUME OF AN OBJECT IS HOW
MUCH SPACE IS INSIDE OF IT,
OR HOW MUCH SPACE IT TAKES UP.
SO FOR EXAMPLE,
IF WE WANT TO FIND
THE VOLUME OF A REFRIGERATOR,
WE MIGHT DO THAT TO FIND OUT HOW
MUCH FOOD MIGHT FIT INSIDE OF IT
IF A BUILDER WANTS TO FIND OUT
HOW MUCH DIRT
THEIR TRUCK CAN CARRY,
THEY MIGHT FIND
THE VOLUME OF THEIR TRUCK.
THOSE ARE JUST A FEW EXAMPLES OF
HOW A VOLUME IS USED
IN REAL LIFE.
NOW, HOW DO WE FIND THE VOLUME
OF THE RECTANGULAR PRISM?
WELL ONE WAY TO THINK ABOUT
IS TO FIND OUT
HOW MANY CUBES OF THE GIVEN SIZE
MIGHT FILL THE PRISM OR FIT
INSIDE OF IT
SO THEREFORE, WE MEASURE VOLUME
IN CUBIC UNITS.
SPECIAL TYPE OF MEASURE
WE USE JUST FOR VOLUME.
IF WE HAVE A CENTIMETRE CUBE,
WHICH MEANS THAT ALL OF THE
EDGES OF THE CUBE
MEASURES ONE CENTIMETRE EXACTLY,
WE CALL THAT ONE CUBIC
CENTIMETRE, OR IN MATH,
WE WRITE THAT AS ONE CENTIMETRE
WITH A LITTLE THREE ON TOP,
WHICH WE CALL A CUBIC
CENTIMETRE.
SO LET'S GIVE IT A TRY
WITH AN EXAMPLE.
On a new screen, a prism pops up next to a set of cubes.
She continues WE CAN USE SPECIAL RULES
TO FIND THE VOLUME OF A
RECTANGULAR PRISMS.
SO LET'S TAKE
THIS PRISM FOR EXAMPLE,
THE FIRST THING I WANT
TO FIND OUT IS,
I CAN SORT OF DIVE UP THE PRISM
INTO A NUMBER OF LAYERS
AND STARTING WITH THE FIRST
LAYER, I'LL ASK MYSELF,
HOW MANY CUBES ARE IN THE
VERY FIRST LAYER?
NOW, I COULD PROBABLY COUNT THEM
INDIVIDUALLY,
SO THAT WOULD BE, ONE, TWO,
THREE, FOUR, FIVE AND SIX,
OR I CAN USE SIMPLE RULES
TO FIND OUT HOW MANY
THERE ARE IN TOTAL.
WHICH FOR ME, I WOULD JUST DO
THE LENGTH, WHICH IS,
THREE TIMES THE WIDTH,
WHICH IS TWO.
SO I'LL DO MY FIRST STEP
OVER HERE.
THE LENGTH TIMES THE WIDTH,
AND THAT GIVES US THE TOTAL OF
SIX CUBES.
NOW THE NEXT PART IS TO JUST
DECIDE HOW MANY LAYERS THERE ARE
JUST LIKE THE FIRST ONE, AND OUR
PRISM OVER HERE,
WE'VE GOT FOUR LAYERS.
SO WE TAKE MY ANSWER FROM
MY FIRST STEP WHICH IS SIX,
AND I JUST MULTIPLY THAT
BY FOUR,
AND IT GIVES ME A TOTAL
OF TWENTY FOUR CUBES.
NOW YOU'LL NOTICE THAT IF YOU
PUT ALL OF OUR STEPS TOGETHER,
REALLY ALL WE DID WAS TO TAKE
THE LENGTH OF THE PRISM,
WHICH IS, THREE, MULTIPLY THAT
BY THE WIDTH, WHICH IS TWO,
AND THEN YOU MULTIPLY THAT
BY THE HEIGHT OF THE PRISM,
WHICH IS, FOUR. SO VOLUME THEN
EQUALS LENGTH TIMES WIDTH,
TIMES HEIGHT.
Using her index finger, she highlights the concepts mentioned on the screen.
She continues OKAY, SO NOW
THAT WE KNOW OUR RULE,
LET'S TRY IT OUT WITH A SIMPLE
EXAMPLE TO TEST IT OUT
AND TO SEE IF IT WORKS.
IF WE WERE ASKED TO FIND
THE VOLUME OF THIS PRISM,
WE'RE GIVEN ITS MEASUREMENTS
ALREADY,
SO THE LENGTH IS
FOUR CENTIMETRES,
THE WIDTH IS THREE CENTIMETRES,
AND THE PRISM HAS A HEIGHT
OF FIVE CENTIMETRES.
NOW USING THE RULE
THAT WE CAME UP WITH,
LENGTH TIMES WIDTH TIMES HEIGHT,
I'M GOING TO PLUG IN
THE NUMBERS THAT I HAVE.
SO THE LENGTH IS
FOUR CENTIMETRES,
MULTIPLIED BY THE WIDTH
OF THREE CENTIMETRES,
AND THE HEIGHT
OF FIVE CENTIMETRES,
AND THAT GIVES ME A TOTAL
OF 60 CUBIC CENTIMETRES.
AND ALL THAT MEANS TVO KIDS IS
THAT THIS PRISM,
TAKES UP 60 CUBIC
CENTIMETRES OF SPACE.
THANKS FOR JOINING ME TODAY,
TVO KIDS.
I'M TEACHER SHAHANA.
AND NOW YOU KNOW HOW TO FIND THE
VOLUME OF THE RECTANGULAR PRISM.
In a colourful TV studio, Shahana stands next to a wall touch screen. She is in her twenties, with shoulder-length brown hair. She wears a blue T-shirt with a print that reads "Home Work Zone" and black trousers.
She says HEY, TVO KIDS.
I'M TEACHER SHAHANA.
AND I'M HERE TODAY TO SHOW YOU
HOW TO FIND THE VOLUME
OF A RECTANGULAR PRISM.
BUT FIRST, WHAT IS VOLUME?
She clicks on a top menu and a definition appears, next to the pictures of a truck and a fridge.
She continues THE VOLUME OF AN OBJECT IS HOW
MUCH SPACE IS INSIDE OF IT,
OR HOW MUCH SPACE IT TAKES UP.
SO FOR EXAMPLE,
IF WE WANT TO FIND
THE VOLUME OF A REFRIGERATOR,
WE MIGHT DO THAT TO FIND OUT HOW
MUCH FOOD MIGHT FIT INSIDE OF IT
IF A BUILDER WANTS TO FIND OUT
HOW MUCH DIRT
THEIR TRUCK CAN CARRY,
THEY MIGHT FIND
THE VOLUME OF THEIR TRUCK.
THOSE ARE JUST A FEW EXAMPLES OF
HOW A VOLUME IS USED
IN REAL LIFE.
NOW, HOW DO WE FIND THE VOLUME
OF THE RECTANGULAR PRISM?
WELL ONE WAY TO THINK ABOUT
IS TO FIND OUT
HOW MANY CUBES OF THE GIVEN SIZE
MIGHT FILL THE PRISM OR FIT
INSIDE OF IT
SO THEREFORE, WE MEASURE VOLUME
IN CUBIC UNITS.
SPECIAL TYPE OF MEASURE
WE USE JUST FOR VOLUME.
IF WE HAVE A CENTIMETRE CUBE,
WHICH MEANS THAT ALL OF THE
EDGES OF THE CUBE
MEASURES ONE CENTIMETRE EXACTLY,
WE CALL THAT ONE CUBIC
CENTIMETRE, OR IN MATH,
WE WRITE THAT AS ONE CENTIMETRE
WITH A LITTLE THREE ON TOP,
WHICH WE CALL A CUBIC
CENTIMETRE.
SO LET'S GIVE IT A TRY
WITH AN EXAMPLE.
On a new screen, a prism pops up next to a set of cubes.
She continues WE CAN USE SPECIAL RULES
TO FIND THE VOLUME OF A
RECTANGULAR PRISMS.
SO LET'S TAKE
THIS PRISM FOR EXAMPLE,
THE FIRST THING I WANT
TO FIND OUT IS,
I CAN SORT OF DIVE UP THE PRISM
INTO A NUMBER OF LAYERS
AND STARTING WITH THE FIRST
LAYER, I'LL ASK MYSELF,
HOW MANY CUBES ARE IN THE
VERY FIRST LAYER?
NOW, I COULD PROBABLY COUNT THEM
INDIVIDUALLY,
SO THAT WOULD BE, ONE, TWO,
THREE, FOUR, FIVE AND SIX,
OR I CAN USE SIMPLE RULES
TO FIND OUT HOW MANY
THERE ARE IN TOTAL.
WHICH FOR ME, I WOULD JUST DO
THE LENGTH, WHICH IS,
THREE TIMES THE WIDTH,
WHICH IS TWO.
SO I'LL DO MY FIRST STEP
OVER HERE.
THE LENGTH TIMES THE WIDTH,
AND THAT GIVES US THE TOTAL OF
SIX CUBES.
NOW THE NEXT PART IS TO JUST
DECIDE HOW MANY LAYERS THERE ARE
JUST LIKE THE FIRST ONE, AND OUR
PRISM OVER HERE,
WE'VE GOT FOUR LAYERS.
SO WE TAKE MY ANSWER FROM
MY FIRST STEP WHICH IS SIX,
AND I JUST MULTIPLY THAT
BY FOUR,
AND IT GIVES ME A TOTAL
OF TWENTY FOUR CUBES.
NOW YOU'LL NOTICE THAT IF YOU
PUT ALL OF OUR STEPS TOGETHER,
REALLY ALL WE DID WAS TO TAKE
THE LENGTH OF THE PRISM,
WHICH IS, THREE, MULTIPLY THAT
BY THE WIDTH, WHICH IS TWO,
AND THEN YOU MULTIPLY THAT
BY THE HEIGHT OF THE PRISM,
WHICH IS, FOUR. SO VOLUME THEN
EQUALS LENGTH TIMES WIDTH,
TIMES HEIGHT.
Using her index finger, she highlights the concepts mentioned on the screen.
She continues OKAY, SO NOW
THAT WE KNOW OUR RULE,
LET'S TRY IT OUT WITH A SIMPLE
EXAMPLE TO TEST IT OUT
AND TO SEE IF IT WORKS.
IF WE WERE ASKED TO FIND
THE VOLUME OF THIS PRISM,
WE'RE GIVEN ITS MEASUREMENTS
ALREADY,
SO THE LENGTH IS
FOUR CENTIMETRES,
THE WIDTH IS THREE CENTIMETRES,
AND THE PRISM HAS A HEIGHT
OF FIVE CENTIMETRES.
NOW USING THE RULE
THAT WE CAME UP WITH,
LENGTH TIMES WIDTH TIMES HEIGHT,
I'M GOING TO PLUG IN
THE NUMBERS THAT I HAVE.
SO THE LENGTH IS
FOUR CENTIMETRES,
MULTIPLIED BY THE WIDTH
OF THREE CENTIMETRES,
AND THE HEIGHT
OF FIVE CENTIMETRES,
AND THAT GIVES ME A TOTAL
OF 60 CUBIC CENTIMETRES.
AND ALL THAT MEANS TVO KIDS IS
THAT THIS PRISM,
TAKES UP 60 CUBIC
CENTIMETRES OF SPACE.
THANKS FOR JOINING ME TODAY,
TVO KIDS.
I'M TEACHER SHAHANA.
AND NOW YOU KNOW HOW TO FIND THE
VOLUME OF THE RECTANGULAR PRISM.
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