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 A Curious Cone (Posted on 2004-10-11)
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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 Open cone | Comment 11 of 12 |

For all you coneheads who want it to be an open cone, it's no big deal to compute it.   The equation changes to:

(r^3)/3 = (r^2)*sqrt(2)
r=3*sqrt(2) = 4.243 for the RADIUS
V=(1/3)pi r^3 = 79.97 for the VOLUME
A=pi*r*s=pi*r*r*sqrt(2) = 79.97 for the AREA

[for an open cone]

Now, seriously though, all this arguing over whether cones are open or closed:   cone't we all just get along?

But the fun part of this problem is that volume can't be equal to area because they have different units.  That's why the problem refers to NUMERICAL area and volume.

 Posted by Larry on 2004-10-11 19:50:00

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