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April 23, 2014

April 23, 2014

Posted by **anu** on Friday, January 7, 2011 at 1:34am.

find the largest volume that such a cone could occupy

- calculus -
**drwls**, Friday, January 7, 2011 at 3:14amLet cone height be h, which is one of the two legs. The base radius will be

R = sqrt(L^2 - h^2)

Volume = (1/3)pi*R^2*h

= pi*(L^2 - h^2)*h/3

Volume is a maximum when dV/dh = 0

dV/dh = pi*L^2 - pi*3*h^2 = 0

L^2 = 3 h^2

Max volume = (1/3) pi*(L^2-L^2/3)*sqrt(1/3)L

= 2*pi*L^3/(9*sqrt3)

- calculus -
**drwls**, Friday, January 7, 2011 at 3:15amLet cone height be h, which is one of the two legs. The base radius will be

R = sqrt(L^2 - h^2)

Volume = (1/3)pi*R^2*h

= pi*(L^2 - h^2)*h/3

Volume is a maximum when dV/dh = 0

dV/dh = pi*L^2 - pi*3*h^2 = 0

L^2 = 3 h^2

Max volume = (1/3) pi*(L^2-L^2/3)*sqrt(1/3)L

= 2*pi*L^3/(9*sqrt3)

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