Figuring Radius of a Cone From Slant Height

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Figuring radius of a cone from slant height will require you to plug your data into a very specific equation. Learn about figuring radius of a cone from slant height with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hi, my name is Marija, and today I'm going to show you how to find the radius of the cone by using slant height. So when we have a cone, the slant height is the height of one of these sides. So let's say that we are given that that height is 5 and if we want to find the radius, the radius is the length from the center of the circle that's in the bottom of the cone over to the edge of the circle. So this is what we are looking for the radius. Then the one other thing that we are going to need is the altitude of the height of the cone so when you are given the altitude, let's say that you are told that it is 4, we can now actually realize that the slant height of the cone becomes the hypotenuse of a right triangle that's within this because when I drop in altitude, it forms a right angle with the circle that's on the bottom. So that means that I can use the Pythagorean Theorem. So I'm going to use A squared plus B squared equals C squared and that's going to help me find the radius. So 5 my slant height is the longest side, it's across from my right angle so that becomes my hypotenuse, so I'm going to substitute C with 5 squared, one of the legs is 4, so I'm writing 4 squared plus B squared equals 5 squared and now when I simplify, I'm going to get 16 plus B squared equals 25 and when I subtract, 16 from both sides I get B squared equals 9 and finally when I take the square root of both sides I get B equals 3. So that means that this radius right here is equivalent to 3.

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