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

Dear Student!

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

Cheers!

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Thank you Sir

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