Show that the semi-vertical angle of the cone fo masimum volume and of given slant height is tan inverse root 2

Dear Student!

Here is the answer to your query.



Let α be the semi vertical angle of a cone of slant height l

Then V O = l cos α and OA = l sin α


Let V be the volume of the cone Then


for maximum or minimum V, we must have


Differentially (1) w. r. t. α we get


The V is maximum when tan α = or α = tan–1


i.e. when the semi vertical angle of the cone is tan–1



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Thank you Sir

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