Find the volume, to the nearest hundredth, of a cone with a slant
height 13 feet and radius 5 feet

Hello.

Once again...

"The volume of a cone is (Pi)r2h/3. Essentially it uses the formula
for the volume of a cylinder and divides it by 3."
source: MathWizz
http://www.mathwizz.com/geometry/help/help2.htm

Slant Height ( Hs ) = SQROOT [ r^2 + h^2 ]
http://microgeometry.netfirms.com/content/cone.html

----------

Here the slant height (Hs) is 13 feet.  So...

Slant Height ( Hs ) = SQROOT [ r^2 + h^2 ]
                13  = SQROOT [ 5^2 + h^2 ]
                13  = SQROOT [ 25 + h^2 ]

squaring both sides:

               13^2 = [25 + h^2 ]
               169  = 25 + h^2
           169 - 25 = h^2
               144  = h^2
                12  = h


Here the radius (r) is 5 feet, while the height (h) is 12 feet.

So... 

Volume = (Pi(5^2)12)/3  
       = (Pi(5^2)12)/3 
       = (Pi(25)12)/3
       = (300Pi)/3
       = 100Pi cubic feet
       = 314.16 cubic feet

-------
search strategy:
"volume of a cone", "slant height"

I hope this helps.