00:0004:00
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00:02: Let's review how to use a scale drawing to find the values in a problem. Suppose we have this drawing of a building, and we have the scale given to be one inch is 30 feet and we wanna first find the length of the blue wall. So what we do is set up a proportion. Easiest thing usually is to set up one that first represents the scale, so we have one inch representing 30 feet. And then set that equal to, to get your proportion a fraction involving the information that you have. So you've been given that the blue wall has a length of three inches and you're trying to find its actual length on the actual building, so give that a value of X and then solve this proportion. So this is just two equal fractions. 130th equals three over X. And the way we would solve that is by cross-multiplying, one times X and 30 times three and that would get us X equals 90. So the answer to the problem would be 90 feet. The thing to always be sure you do is keep the units in the same locations in your proportion. So if you have 1 inch over 30 feet then make sure you have inches over feet in the other faction in your proportion. 01:33: Suppose we're looking for the length of the red wall, again, we would use our ratio that represents the scale, which is one inch to 30 feet and then we've been given eight inches as the length in the drawing so put that over X feet cross, multiply one times X, 30 times eight, so the red wall, would be 240 feet long. Suppose now we wanna find the length of the green wall. Well, then we'll have one inch to 30 feet, equals 1.5 inches to X feet and we'll have one times X again, and 1.5 times 30, which is 45 feet. 02:34: Now, let's suppose that someone comes along and tells us that this wall is actually 180 feet in real life, and we wanna determine how long we should make the drawing of it. How long would the drawing be to maintain this scale? But we can actually solve that the same way. We'll just suppose this is the black wall and we're going to use our scale, which is one inch to 30 feet. But in this situation, we've been given the number for the feet, so we're gonna put the 180 in the denominator, and in this case have the X in the numerator, because it's that that we don't know. We cross multiply again, one times 180 and 30 times X. And so now, we get an equation that isn't quite solved for X, we've got one more step to do, which is to divide both sides of the equation by 30, and then we get X equals six. 03:44: So in this case, the 6 would not represent feet as it did in the other problems, but would represent inches because it's going to go here and that would be the length of the drawing. We would have to have six inches in the drawing to represent 180 feet.
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Question 1
The blue wall was ___ feet long.
Responses
A 6060
B 9090
C 120120
Question 2
The red wall was ___ feet long.
Responses
A 120120
B 180180
C 240240
Question 3
The black wall was ___ inches long in the drawing.
Responses
A 66
B 88
C 1010
Question 1:
The blue wall was 90 feet long.
Question 2:
The red wall was 240 feet long.
Question 3:
The black wall was 6 inches long in the drawing.
00:0002:50
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00:02: Let's review the idea of the circumference of the circle and how to find it. Remember that the circumference of a circle is the distance around the circle. It's kind of like the idea of perimeter when you're dealing with polygons like rectangles and hexagons, but of course there are no angles and there are no straight line segments. 00:24: Now, if you remember the special number pie which we often just represent with 3.14, pi is a ratio. It's a very special ratio. It's the ratio of the circumference of a circle to its diameter. So remember that a diameter is a chord which is a line segment that passes through the center of the circle. So pi is actually defined to be the total length around the circle, the circumference divided by the diameter. Now, from that little definition, if we just imagine multiplying both sides by D, we can see that the circumference is equal to D times pi or pi times the diameter. 01:18: Now, in a lot of applied situations, you don't have the diameter, but rather the radius And of course remember, the radius is just half of the diameter. It's this length from the center of the circle out to the circle itself. And I'm just gonna go ahead and label that R. So the radius is just half of the diameter. So another formula that we use when we're finding the circumference is circumference equals 2 pi R. And what we've done there is we've multiplied pi by the radius, but that we've had to double it because the radius is only half of a full diameter of the circle. 01:58: So let's take a specific case where we have a circle and we're given that its radius is 3 centimeters. That if we wanted to find the circumference, we would use the formula 2 pi R. And so we'd have 2 times pi times the radius which is 3. And if we multiply those together and just keeping the pi as itself so that we have the exact value, we end up with 6 pi and then that would be centimeters. And if you want to get a numerical decimal approximation, you can use 3.14 or whatever approximation you're told to use and then just multiply that way and you would end up getting 18.84 centimeters.
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Question 1
C = 2(pi)r and C = d(pi) are the formulas for finding the _____________ of a circle.
Responses
A RadiusRadius
B AreaArea
C CircumferenceCircumference
Question 2
What is the radius of the circle in the example?
Responses
A 3 cm3 cm
B 5 cm5 cm
C 7 cm7 cm
Question 3
What is the circumference of the circle in the example?
Responses
A 2π2π
B 4π4π
C 6π6π
Question 1:
C = 2(pi)r and C = d(pi) are the formulas for finding the Circumference of a circle.
Question 2:
The radius of the circle in the example is 3 cm.
Question 3:
The circumference of the circle in the example is 6π.