WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over the circumference of a circle.
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First let's go over some special segments within circles; the first is the radius.
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Radius is a segment whose endpoints are on the center and on the circle.
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One endpoint is on the center; the other endpoint is on the circle.
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Here this segment CB or BC, doesn't matter which way, is a radius.
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CA, that is also radius; I can say CA; I can say CB; I can say EC.
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Those are all radius; each of those are radius; plural for radius is radii.
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The next special segment is the diameter.
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Diameter is a segment whose endpoints are on the circle.
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It has to pass through the center.
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It is like two radius put together like this back to back
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to form a straight segment where each of the endpoints are on the circle.
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That is a diameter; here EB, that is a diameter.
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That is the only one for here.
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DF, even though that segment has endpoints on the circle, it is not passing through the center.
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So that is not considered a diameter.
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That is actually called a chord; chord is like a diameter.
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Diameter and chords, they both are similar in that they have their endpoints on the circle.
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But diameter has to pass through the center; chords do not.
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This is a chord; this is a diameter.
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Again this is a radius; radius; this is a diameter; chord, this is a chord.
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Endpoints on the circle without passing through the center, that is a chord.
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The circumference is like perimeter.
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We know perimeter is when you add up all the sides of some polygon.
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Circumference acts as a perimeter.
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But it is like the perimeter of a circle because circles, we don't have straight sides.
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Instead of calling this perimeter, we call it circumference.
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But it is pretty much the same thing; it is like you wrap around.
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It is like if we need to build a fence around this garden.
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We would call that perimeter because you are going around like this.
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Let's say your garden is round like this.
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Then it is not called perimeter anymore; it is called circumference.
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But it is the same concept, same idea; distance around the circle.
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You find that by multiplying the radius by 2 and multiplying that by π.
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It is 2 times π times the radius.
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When you multiply numbers together, see how we are just multiplying three numbers together.
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2 and the π and the radius.
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Whenever you multiply, it doesn't matter the order.
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If we want, we can do 2 times π times the radius.
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Or we can do radius times 2 times π or π times radius times 2.
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The order doesn't matter when you multiply.
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In short, this is circumference; it is 2πr; 2πr.
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Since the order doesn't matter, since we are multiplying these three numbers together,
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I can do 2 times r times π.
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2r; if I take a radius and I multiply it by 2... that is one.
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Here is another one; this is 2 times the radius.
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R plus r is same thing as 2 times r; doesn't this become the diameter?
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If we take 2 radius, this can also be diameter.
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We can also say circumference is diameter times π; this actually has two formulas.
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Circumference can be 2 times the π times the r.
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Or it can be, since 2 times r equals the diameter, 2 times the radius is the diameter.
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We can just say the diameter times π.
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Doesn't matter which one we use; it depends on what they give us.
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If we are given the radius, then we can just use 2πr.
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They give us the diameter; you can just go ahead and multiply that by π.
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Since you have to divide it, find the r, and then you have to multiply the 2 anyways.
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If you are given radius, just use that.
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If you are given diameter, just use that.
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Again 2 times the π times the radius; π is 3.14; 3.14.
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It is actually longer; but you only have to use 3.14.
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The first example, we are going to name the given parts of the circle.
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First is the chord.
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Remember chord is a segment whose endpoints are on the circle.
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But it doesn't pass through the center.
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There is an endpoint on the circle; there is an endpoint on the circle.
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A chord, you can say ED; it doesn't matter if I say DE.
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Or I can say AB or BA.
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The diameter, both endpoints on the circle; one, two; it passes through the center.
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BE would be diameter; another one, AD is a diameter.
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For radius, remember radius is endpoint on the center, endpoint on the circle.
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That would be a radius; I can say CD; I can say BC.
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I can say AC; I can say EC; I can say CE.
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Find the circumference of the circle; this in the circle, this is the center.
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This is the radius; this is the radius; it is 5.
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The circumference of a circle is 2 times π times r, the radius.
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It is 2 times, π is 3.14, times 5.
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If you want, we can multiply this and this first.
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Remember the order doesn't matter; it doesn't matter.
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You can multiply this times this and then to that; it doesn't matter.
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But I know that if I multiply 2 times the 5, then I get 10.
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10 is an easy number to multiply with; C is 10 times 3.14.
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I need to multiply these two numbers together; 3.14 times 10; 0.
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1 times 4 is 4; 1 times 1 is 1; 1 times 3 is 3.
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From here, since I am multiplying, how many numbers do I have behind decimal points?
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I only have two.
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I am going to in my answer put the decimal point in front of two numbers.
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It is 31.4 or 31.40; it is the same thing.
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I can just drop the 0 if I want to because it is behind the decimal point and at the end of a number.
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Circumference is 31.4 or 31.40.
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When I multiply by 10, there is a shortcut way of doing this.
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When you multiply by 10, you see how many 0s there are.
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10 has only one 0; you take the decimal point.
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You are going to move it one space because there is one 0.
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To determine if you are going to move it to the left or to the right,
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if we are multiplying, don't we have to get a bigger number if we are multiplying by 10?
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Our number has to get bigger.
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If I move the decimal point to the left, my number is going to get smaller because 0.3 is not the same.
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I want a bigger whole number.
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I have to move it to the right to make my number bigger.
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It is going to be 31.4.
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Let's say I am going to multiply by 100; 100 has two 0s.
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Then you would move it two spaces to the right to make it bigger.
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It is going to be one, two; it is going to be 314.
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That is going to be my answer; that is my circumference here.
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Let's move on to the next problem.
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Find the circumference of each circle with the given measure.
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The first one, the radius is 9 inches.
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Circumference equals 2πr, 2 times π times r.
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2, π is 3.14, the radius is 9.
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Again I like to multiply these two numbers first; you don't have to.
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You can multiply this times this and then take that and multiply it to this again.
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18; 2 times 9 is 18; times 3.14.
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Now I have to multiply these two numbers; it is 3.14 times 18.
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4 times 8 is 32; times 1 is 8; plus 3 is 11.
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This is 24; 25; 1 times 4 is... I put a 0 up there.
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1 times 4 is 4; 1 times 1 is 1; 1 times 3 is 3.
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I can go ahead and add; 2 plus 0, 2.
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This is 5; this is 6; this is 5.
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Within my problem, how many numbers do I have behind decimal points?
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I have two; from here, I am going to go one, two.
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Place two numbers behind the decimal point for my answer.
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My circumference becomes 56.52 inches.
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It is not inches squared; only area is squared, units squared.
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Circumference, you just leave it as 62.52 inches.
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The next one, the diameter is 16 centimeters.
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Remember if this is the formula, 2 times r becomes the diameter.
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2 times radius is diameter.
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I can just go ahead and say this formula is the same thing as diameter times π.
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Diameter is 16; 16 times 3.14; here 3.14 times 16.
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6 times 4 is 24; 6 times 1 is 6; plus 2 is 8.
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6 times 3 is 18; place the 0 there; 1 times 4 is 4.
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Times 1 is 1; 1 times 3 is 3; add; this is 4.
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8 plus 4 is 12; 8, 9, 10; 3, 4, 5.
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From here, I have two numbers total behind decimal points.
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I am going to go one, two; for this one, my circumference is 50.24 centimeters.
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My circumference here; and this is my circumference here.
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That is it for this lesson; thank you for watching Educator.com.