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A Curious Cone (Posted on 2004-10-11) Difficulty: 2 of 5
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.

See The Solution Submitted by Jer    
Rating: 2.2500 (4 votes)

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Solution Solution | Comment 4 of 12 |
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

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