A Curious Cone (Posted on 2004-10-11)

	Submitted by Jer
Rating: 2.2500 (4 votes)
Solution:	(Hide)
r = h = 3+3sqrt(2) S.A. = V = (39+43sqrt(2))*pi l = slant height = sqrt(r^2+h^2) = sqrt(2)*r S.A. = pi*r^2 + pi*r*l V = (1/3)*pi*r^2*h Replace h with r, set S.A. = V and simplify to get r^3 - 6r^2 - 9 r = 0 Factor out r and solve via quadratic equation to get r. Substitute r back into volume formula for V. ***As a geometry teacher I can verify that Surface Area is different from Lateral Area. Only the former counts the circular base.*** ***As a geometry teacher I am embarassed at not pointing out that the cone is a right cone. I don't know of any S.A. formula for an oblique cone.***

	Subject	Author	Date
	re: Open cone	Fletch	2004-10-12 10:50:44
	Open cone	Larry	2004-10-11 19:50:00
	re: Seriously, though.....	David Shin	2004-10-11 15:33:26
	Seriously, though.....	Penny	2004-10-11 14:55:03
	re(3): More info required !	Penny	2004-10-11 14:11:06
	re(2): More info required !	nikki	2004-10-11 13:11:54
	A solution	nikki	2004-10-11 13:07:23
	re: More info required !	Penny	2004-10-11 12:15:21
	Solution	Larry	2004-10-11 11:50:23
	More info required !	Syzygy	2004-10-11 11:48:43
	Solution (I think...)	Penny	2004-10-11 10:11:10
	Solution	Fletch	2004-10-11 09:57:57