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Surface Area of a Cone-Geometry Help-MooMooMath

2,614 views · Published 13 January 2013 · 3:41 · Indexed 30 September 2026

Channel: MooMooMath and Science · 2013 · Education

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Surface area of a cone explained. The surface area of a cone is found by finding the lateral area and adding this to the base area 

Transcript
Surface Area of a Cone
Hi Welcome to MooMooMath. Today we are going to look at the surface area of a cone. What is the surface area? It is the outside covering of the cone. So if you are eating an ice cream cone it is the shell plus a top or a lid that sits on it because it has a base at the bottom. So let's look at these two parts. If I were to take this cone and cut it open it would look something like this. (Draws a curved object) and then we have the circular base. The sides of the cone is the lateral area, and then we have the circular base. For a cone you only have one base. Now for the formula we have two parts. We have πr^(2 ) S and πr^ (2) so what is the π r squared s. It is the lateral area of the cone. R stands for the radius and s stands for the slant height. That is not the height of the cone but the height of the slant. I will show you how to find that. If our radius is 6 and our height is 8 our slant height is this measurement out here. (Draws on the cone shape) it is the side of the cone. So since this is a right triangle I can use the Pythagorean formula to solve for it. So I take A squared plus B squared so I take 6 squared plus 8 squared is 36 plus 64 which is 100 and the square root of 100 is ten. So my slant height is 10. So I will multiple π times the radius of 6 squared times 10 which equals 360 π. So that gives me my lateral area. Now let's add the area of the base which is simply πr^2 We have already defined the radius as 6 so 6 squared is 36 πand we will add those two together and get 396 π and this is area so it is units squared. So let's look over the rules.
The formula for surface area of a cone is:
 pi *radius squared + slant height + pi *radius squared 
h = height 
r = radius
s= slant height (The side of the cone)
Here is an example, if our radius is 3 and our height is 4 we use our Pythagorean Theorem 16 the square root of four plus the square root of 25 is 5 to find the slant height we plug it all in and in this example it is 54 units squared. Hope this was helpful. 

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https://www.youtube.com/watch?v=9G5AxYl3wr0

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