Bài 25 Volume of a Cube- Thể tích hình lập phương

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Boys and girls ,

Ladies and gentlemen.

Today  we will be finding the volume of a cube.

First  we should probably talk about what a cube is .

A  cube is basically a box that has six congruent or equal squares.

So  all of the squares that form the cube are exactly the same.

So  what do we mean by volume .

So  here we have a three-dimensional object and this is really the first three dimensional object .

We 've been dealing with when we talk about volume it's .

How  much would fill up the entire cube like if we wanted to pour water into this cube.

How much water would fill up the cube.

So volume is all of the space that's taken up by the inside of the cube.

We're going to use volume when we're talking about any three dimensional object.

So we want to find the volume of this cube .

Now you have to know one of your side lights so.

Here this is six inches.

Now remember because this is a cube this is a three-dimensional object.

That 's created by six identical squares nino and a square.

You are.

Face  in the height of the square exactly the same .

So if that's six inches , this is also six inches .

This 6 inches.

This is six inches really all of the lines you see or six inches.

So when we're finding volume and we first want to find the area of our base which is the square that on the very bottom here.

The first thing we want to do is find the area of the square that is the base of the square.

Remember the space of the square is the square that's on the bottom.

But Now we know that one side length of the square is fixed .

So  the other side length of the square also has to be 6.

And  therefore the area of this square will be 6 times 6 or 36 square inches.

 To  find the volume we're going to multiply the area that is the area of the base.

Times  our height which again in this case is going to be another six inches.

So the volume here of our cube is going to be 216 cubic inches or inches cubed.

Whenever  we're finding the volume of a rectangular prism which

is basically anytime,  you have a three-dimensional figure that's contained by rectangles.

You're going to find the volume by length times width times height now.

Because  this is a cube, our length or width and our height all have the same length.

And  therefore we can say that it is our side length cubed or the side length to the third power.

And  now remember ,because we're talking about volume ,our answer always has to be in our units cubed or to the third power.

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Bài 24 Volume - Rectangular Prisms - thể tích lăng trụ hình chữ nhật.

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Volume is measured by how many cubic units it would take to fill a given space.

The  cube shaded green is a cubic unit .

The amount of cubic units it takes to fill a defined space is what we call volume .

The shown geometric solid is a rectangular prism .

To find the volume of any rectangular prism, we simply multiply the length times the width times the height .

The length and the width of the rectangular prism are always at the bottom of the shape.

These  two dimensions make up the base of the rectangular prism.

In this case the length is 4 in the width is 3.

Multiplying  the length times the width will give you the area of the prisms base .

This is a two dimensional measurement .

After multiplying the length times the width and getting the area of the rectangular prisms base by multiplying it by the rectangular prisms height that will give us the volume.

Multiplying  the area of the prisms base by the height is filling up the prism or adding depth .

This is what gives our rectangular prism a third dimension or gives it volume.

We  can clearly see when multiplying the length times the width of the rectangular prism.

We come up with 12 square units which would be the area of the rectangular prisms base.

Remember this is only a two dimensional measurement.

To  give a depth or volume we must now multiply the area of the rectangular prism space of 12 by whatever the height is to fill up the rectangular prism or to add depth or volume.

 If  we multiply the area of the base which is 12 by a height of 1 that would give us 12 cubic units which would be how many cubes it would take to make one level of our rectangular prism.

Adding  two levels of 12 we would get a total of 24 cubic units three levels of 12 would give us 36 four levels of 12 give us 48 cubic units.

And  of course five levels of 12 would give us 60 cubic units.

We could say that each level of the rectangular prism contains 12 cubes.

There  are five love twelve cubes for a total of 60

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Bài 23 Pie Chart-biểu đồ hình quạt

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LESSON 12

Pie chart .

A  pie chart presents the data in the form of a circle that is

divided into sections .

Each section corresponds to a particular data value.

The area of each section is proportional to the proportion of the category that section represents .

Pie charts are primarily constructed for qualitative data where the relative size of each section depicts the percentage.

So  here is an illustration of a generic pie chart  where like all graphical methods a descriptive title appears at the top.

Then  each individual section is clearly labeled with the corresponding data value and percentage .

The relative size of each section depicts the percentage of each category.

 For  instance, the entire pie or circle accounts for 100% of the data.

 If  we're to cut this 100% in half, we would then show 50 50 % slices .

If  you cut the halves in half ,we then have quarters or 25 percent segments of the pie.

So the overall relative size of each piece corresponds to the percentage that that data value occupies.

Here  cutting the 100% into thirds, we get 33  33 % sizes.

Or  other various sizes 10%, 15% together make 25%, 20%, 30% together make up 50%.

In  statistics drawing a pie chart by hand is rarely done.

In  practice ,pie charts are constructed using software applications.

To  describe the distribution of qualitative data represented in a pie chart , the various categories observed are merely mentioned along with their associated percentages.

This  is because qualitative data that's at the normal level doesn't follow a particular order and using the conventional terms like bell-shaped or skewed do not apply to this type of data.

So  when describing the pie chart,  you merely just mention the categories along with their associated percentages.

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BÀI 22 : Convert Mixed Numbers to Improper Fractions – đổi hỗ số sang phân số không thực sự

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Converting mixed numbers to improper fraction .

Let 's try and convert one and three fourths to an improper fraction.

Let 's represent this in the form of squares .

Now  let's try representing the squares as a fraction .

Counter  the scraps.

There  are seven fourths that is 7 over 4.

So  1 and 3 fourths equals seven folds.

To change a mixed number into an improper fraction .

Multiply  the old number by the denominator.

And  add it to the numerator of the fractional part.

Let 's do one more and this time without the help of any squares or pictures .

Let 's change 2 and five sixths to an improper fraction.

First multiply 2 by 6 that is multiply the whole number by the denominator .

Then  add it to the numerator of the fractional part which is five.

Hence  17 becomes our new numerator .

The  denominator remains the same which is six .

Hence  our improper fraction becomes  17 / 6.

Let 's look at one more example.

Six  and a half .

So  it is  6 x 2 plus 1 equals 30.

Denominator  remains too.

Hence  the improper fraction is 13 by 2 .

Did n't I tell you it was easy.

Now  let's look at..

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Bài 21 Improper Fraction- phân số không thực sự.

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Improper fractions.

Improper  fractions have  the numerators that are larger than or equal to the  denominators.

 11 / 4    5 over 5  and 13 / 2 are some improper fractions .

Let 's look at an example.

This hexagon has seven pieces .

Hence  this fraction will be written as 7 over 6.

So we see that the numerator is greater than the denominator

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BÀI 20 : Mixed Numbers – Hỗn số

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Shh

Mixed numbers .

Fractions  are used to count a part of something.

Mixed  numbers are used when you need to count whole things and parts of things at the same time .

How  much of these squares is red.

There  are three whole squares and one-fourth of another square.

We  write it like this 3 1/4 and read it like 3 and 1/4 .

It 's really 3 plus 1/4 but we don't put the plus in .

This  is why we say the and.

Hence  we see that mixed numbers have a whole number part and a fraction part.

Examples  2 and 3/4 and 6 and ½.

You  are right .

This  is really getting to be interesting and fun .

Now  let's look at

Ummh

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