There is a cone whose radius is equal to its height. The numerical surface area is equal to the numerical volume. Find the exact radius and volume of the cone.

Volume = (pi * r^3)/3        since height =r
Surface area = pi * r^2  +  pi * r * s    where s is the slant height
Slant height is r*sqrt(2)
Surface area = pi r^2 * (1+sqrt(2))
Vol = Area     divide both sides by pi r^2
r/3 = 1+sqrt(2)
radius= 3*(1+sqrt(2)) = 7.243
Vol =  397.8
Area =   397.8

Haven't checked others yet
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Edited to show:  Fletch had it right first

Edited on October 11, 2004, 11:52 am

Posted by Larry on 2004-10-11 11:50:23