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January 26, 2015

January 26, 2015

Posted by **Mishaka** on Friday, December 16, 2011 at 7:43pm.

- Calculus -
**Mishaka**, Friday, December 16, 2011 at 8:13pmPretty sure I figured it out, 4/27. I found this by simplifying:

((1/3pi (h - 2/3 h))(4/9 r^2)) / (1/3 pi r^2 h)

- Calculus -
**JWAL**, Thursday, December 22, 2011 at 6:06pmHow did you get this? Please help I am stuck.

- Calculus -
**Steve**, Sunday, January 22, 2012 at 4:37pmDraw the cones. If the large cone has height H and radius R, the small cone has height h and radius r, so that

r/R = 1 - h/H

The ratio of the two volumes is v/V = r^2h/R^2H = (r/R)^2 h/H

if we maximize that ratio as a function of u = h/H, we get

f(u) = (1-u)^2 * u

= (u - 2u^2 + u^3)

f'(u) = (1-4u+3u^2)

= (h-1)(3h-1)

Clearly, when u=1, f(u) = 0 a minimum

when u = 1/3, f(h) = 4/9*1/3 = 4/27

so, h/H = 1/3 for max volume ratio

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