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