



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 
