0:00
All right.
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For this problem, we have a waffle cone with a diameter of 3 .5 inches.
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So that means it has a radius of 1 .75 inches and it has a height of 8 inches.
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And we want to know how much waffle we need in order to wrap it around and make this cone.
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So that is a surface area problem.
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Specifically, it is a lateral surface area problem.
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And what that means is in a normal surface area for a cone, we would take into account the area of that circular bottom.
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But for our cone, that's open, that's a hole.
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So we don't have to consider that.
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So our formula for lateral surface area is going to be times the radius times the slant height.
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So the slant height is this side here, this slanty side of the cone.
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Cone.
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We want to know what that measure is.
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And you can see that with the radius and the true height of the cone, we have made a right triangle.
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So what we can do is we can use the measurements that we have.
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So we know this is a length of 1 .75 and this is a length of 8.
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We can use pythagorean theorem to figure out what our missing side is.
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So we can say 1 .75 squared plus 8 squared is equal to our missing side squared.
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I'm just using s because that's what's in our lateral surface area formula here.
01:26
Alright so 1 .75 squared is 3 .0625.
01:32
8 squared is 64.
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That's going to equal our s squared.
01:36
So i'm going to add these two together and that's going to give me 67 .0625 equal to s squared.
01:45
I'll take the square root of both sides because i don't want s squared.
01:49
I want s by itself.
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Now of course 67 .0625 does not have a perfect square but we're going to see what it's about.
01:59
So s is going to be about 8 .189.
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I'm going to go ahead and leave it at three decimal places.
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I know at the end we're going to round to a whole number but we want to save that for as close to the end as we can.
02:13
So going back up here to our lateral surface area formula, we know pi, we know the length of the radius, and now we know the length of the slant height, 8 .189.
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So put all of this into your calculator that has a pi button.
02:30
Don't substitute 3 .14 as pi.
02:32
Use the pi button on your calculator because then you'll get a truer rounding.
02:38
So we're going to get a lateral surface area that's equal to 45 .02.
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Two.
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We want to round to the whole number...