Geometry Finding the Area of a Cone
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Cone Heads
Finding the Area of a Cone

 

 Remember the formula for the volume of a cone?

 The volume of a cone uses the same formula
 as the volume of a pyramid.
 

 
 Example:
 Find the volume of this cone ...
 

 
 The formula for the surface area of a cone
 uses the idea of the slant height.
 
 If we know the radius and the height of a cone,
 we can find the slant height.
 To do this, look at a cone straight from the side.
 

 
 The height and the radius of the cone
 are the legs of a right triangle.
 
 You can find the slant height
 using the Pythagorean theorem.
 

 

 
 The surface of the cone is equal to 
 the circumference of the base
 times the slant height times 1/2.
 For our cone we have:
 

 

 
 If you look back at the pyramid page
 you will see that these formulas work there too.
 In fact, the shape of the base does not matter.
 The same formulas give us the volume 
 and the surface area.
 

 

 

   copyright 2005 Bruce Kirkpatrick

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