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Hello there.
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In this problem, we're being asked to find the slant height of a right cone with a radius of five inches and a surface area of 61 pi inches squared.
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So we'll draw a cone here.
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Remember, a right cone is basically a cone that's standing straight up.
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So if we draw the height, i'm just going to make some notes here, draw the height in, and that's going to make a 90 degree, a perpendicular angle with the base.
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So that's a right cone.
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And what we're looking for is the slant.
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Which is height from the base of the vertex, and we'll call that l.
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So remember a couple of things.
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The surface area of this cone is going to equal the base area plus the lateral area.
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So what are we talking about there? the base area is this flat part on the bottom, and then this lateral area is the side, the side that wraps all the way around the cone.
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Think about an ice cream cone, that's the cone part, and then the base would be open.
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So that's the lateral surface area.
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So in this problem, we know we're given the surface area 61 pi inches squared.
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And we were given the radius of five inches.
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So the radius kind of getting messy here, but that's the radius, just like you've seen a radius before.
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And so we can, and then one more thing we know that it's going to help us out here.
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The lateral area, remember that's the part in blue there, is going to be equal to pi times the radius times the slant height, l.
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And that's what we're looking for.
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So once we find this lateral surface area, a big l, we know pi, we know the radius, we can find little l.
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So let's work on next finding out what this is.
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Let's figure out what the lateral surface area is.
02:15
Well, the good news is we know s and we can find b...