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OK, you are right, the answer should be 2\sqrt{2}/\sqrt{3} π
Let the cone angle be θ, then the volume is expressed as (π l^3 sin^2 θ cos θ)/3
Set t=cos θ, then the volume = (π l^3 / 3)(t-t^3), where t∈[-1,1]
Taking derivative gives t=1/\sqrt{3} should be the maximum point,
which implies the desired result.
Let the cone angle be θ, then the volume is expressed as (π l^3 sin^2 θ cos θ)/3
Set t=cos θ, then the volume = (π l^3 / 3)(t-t^3), where t∈[-1,1]
Taking derivative gives t=1/\sqrt{3} should be the maximum point,
which implies the desired result.
5楼2015-02-11 00:44收起回复
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